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Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Of the following values of n, the value of (-1/7 )^(-n) will be greatest for n = options: A)3 B)2 C)0 D)-2 E)-3 SOLUTION:imo -2 (-17)^-2= 1/(1/49)=49 oops i meant 2 B #### B QUESTION:If 1/(x+2)+1/(x-2)=1/(x+2), what is the value of x? options: A)-1 B)2 C)1 D)-2 E)0 SOLUTION:If we solve the question, we get x=-2. Option: D #### D QUESTION:A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss? options: A)17 B)15 C)11 D)16 E)12 SOLUTION:CP of 20 dozen of bananas = 15 * 20 = Rs. 300 Number of bananas which are rotten = 1/4 * 20 = 5 dozen. SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225 SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75. SP of 1 dozen bananas = 75/5 = Rs. 15. Answer: B #### B QUESTION:76^77 /7 remainder is ? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:as, 4^3/3=64/3 remainder=1 and also 4/3=1 and 5^3/3 remainder=2 and also 5/3=2 so it does not matter on the power value so the answer will be 76/7 remainder=6 ANSWER:B #### B QUESTION:Rakesh credits 15% of his salary in his fixed deposit account and spends 30% of the remaining amount on groceries. If the cash in hand is Rs.2380, what is his salary? options: A)Rs.3500 B)Rs.4000 C)Rs.4500 D)Rs.5000 E)None SOLUTION:Explanation: Let salary be Rs.x. Then, x-15% of x -30% of 85% of x = 2380 or x- 15x/100−30×85×x/100×100=2380 or 200x-30x-51x=2380×2002380×200 or 119x = 2380×2002380×200 or x 2380×200/119=4000 Correct Option: B #### B QUESTION:how many square are there between 2001....2300 I don't remember the exact series. options: A)1 B)4 C)2 D)3 E)5 SOLUTION:series was from 2001 to 2300 45^2=2025 46^2=2116 47^2=2209 48^2=2304 (so exclude 48) so ans is 3 (45,46 and 47) ANSWER:D #### D QUESTION:The sum of two numbers is 16. The difference is 4. What are the two numbers? options: A)10-6 B)8-8 C)9-7 D)11-5 E)13-3 SOLUTION:Let x be the first number. Ley y be the second number x + y = 16 x - y = 4 Solve the system of equations by elimination Adding the left sides and the right sides gives: x + x + y + -y = 16 + 4 2x = 20 x = 10 Since x + y = 16, 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 The numbers are 10 and 6 correct answer is A)10-6 #### A QUESTION:The difference of two numbers is 1515. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ? options: A)A)270 B)B)280 C)C)290 D)D)300 E)E)310 SOLUTION:Let the smaller number be x. Then larger number = (x + 1515). x + 1515 = 6x + 15 5x = 1500 x = 300 Smaller number = 300. D) #### D QUESTION:If n is an integer, which of the following CANNOT be a factor of 3n+4? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:3n+4=3(n+1)+1 cannot be a multiple of 3, it's 1 more than multiple of 3: ... 4, 7, 10, 13, 16, ... Hence it cannot be a multiple of 2*3=6 as well. Answer: C. #### C QUESTION:At what rate percent on simple interest will a sum of money double itself in 20 years? options: A)2% B)6% C)3% D)4% E)5% SOLUTION:P = (P*20*R)/100 R = 5% ANSWER:E #### E QUESTION:A goods train runs at the speed of 72 km/hr and crosses a 150 m long platform in 26 sec. What is the length of the goods train? options: A)299 B)277 C)276 D)370 E)281 SOLUTION:Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 150)/26 = 20 x = 370 m. Answer: D #### D QUESTION:Pants, Shorts and Shirts in a dresser are in the ratio of 7: 7: 10. If there are 14 Pants, the number of Shirts in the dresser is: options: A)14 B)7 C)20 D)70 E)35 SOLUTION:Explanation : Let Pants = 7x, Shorts = 7x & Shirts = 10x. Now, 7x = 14 hence x = 2. Number of Apples = 10x = 20. Answer : C #### C QUESTION:If m and n are positive integers, and m=2n and k=9m, then - options: A)k is a factor of m. B)2m is a factor of k. C)3m is a factor of k/2. D)m/2 is a factor of k. E)k is a factor of m/2. SOLUTION:m=2n --> m is even. k=9m --> m is factor of k, thus m/2 = integer must also be a factor of k. Answer: D. #### D QUESTION:If 5^10 x 2^10 = 10^n what is the value of n? options: A)16 B)14 C)12 D)10 E)18 SOLUTION:5^10*2^10 = 10^n or 10^10 =10^n n=10 D #### D QUESTION:Milk contains 5% water. What content of pure milk should be added to 10 liters of milk to reduce this to 2%? options: A)10liters B)15liters C)20liters D)18liters E)22liters SOLUTION:Quantity of water in 10 liters = 5% of 10 liters = 0.5 liters Let x liters of pure milk be added. Then, 0.5/(10+x) = 2/100 2x = 30 x=15 liters Answer is B #### B QUESTION:Carmelo and LeBron participate in a six-person footrace on the basketball court during All-Star Weekend. If all six contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron? options: A)5040 B)2520 C)360 D)120 E)42 SOLUTION:6! = 720 720/2=360 half the time carmelo is in front, vice versa Answer: (C) 360 #### C QUESTION:How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? options: A)5 B)4 C)20 D)25 E)30 SOLUTION:Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it. Required number of numbers = (1 x 5 x 4) = 20. ANSWER C #### C QUESTION:Three numbers are in the ratio 5 : 6 : 8. The sum of its longest and smallest numbers equals the sum of the third number and 49. Find the third number? options: A)A)54 B)B)75 C)C)48 D)D)42 E)E)63 SOLUTION:Let the numbers be 5x, 6x, 8x. Largest number = 8x. Smallest number = 5x. Third number = 6x. 8x + 5x = 6x + 49 7x = 49 =>x=7 6x=42=> third number is 42. Answer:D #### D QUESTION:In 1999, there are 28 days in February and there are 365 days in the year. In 2000, there are 29 days in February and there are 366 days in the year. If the date March 20, 1999 is a Wednesday, then which one of the following would the date March 20, 2000 be? options: A)Friday B)Tuesday C)Monday D)Sunday E)Saturday SOLUTION:From the information given, March 20, 2000 is 366 days after March 20, 1999. 366 days = 52 weeks and 2 more days. Therefore if March 20, 1999 is a Wednesday, then March 20, 2000 is Wednesday + 2 days = Friday Answer: A #### A QUESTION:Consider a sequence of numbers given by the expression 7 + (q - 1) * 5, where n runs from 1 to 80.What is the sum of this series ? options: A)409 B)1636 C)16360 D)16000 E)15360 SOLUTION:terms in this sequence are 7,12,17----402 now since this is an a.p. with a common difference of 5. therefore its sum can be given as q(a+l)/2----------------1) q= total no. of terms =80 a= first term=7 l= last term=402 subsituting values in the expression 1 we have 80(7+402)/2 = 40(409) =16360=C #### C QUESTION:What is the value of m and n ? if log3m/log3n=log 52 options: A)1,5 B)2,5 C)3,5 D)4,5 E)2,3 SOLUTION:log (base a) b=log(base n)b/log(base n)a here base are same in reverse way of formula so log(base n)m=log(base 5) 2 hence n=5,m=2 ANSWER:B #### B QUESTION:In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 16 percent of revenues. The profits in 2009 were what percent of the profits in 2008? options: A)80% B)105% C)120% D)124.2% E)128% SOLUTION:x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,16 = 16/100 x= 80*16/100 x= 12.8 12.8/10 = 1,28 = 128%, Answer E #### E QUESTION:List I: 3, 6, 14, 19 List II: x, 3, 14, 8, 19 options: A) 6 B) 7 C) 8 D) 9 E) 10 SOLUTION:We start by calculating the median of the numbers of list I: 3, 6, 14, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers. median = (6 + 14)/2 median = 20/2 median = 10 The median of list I is 7. Looking at list II: x, 3, 6, 14, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 10 and therefore x is 10. The answer is E. #### E QUESTION:Bat is bought for Rs.400 and sold at a gain of 20% find its selling price? options: A)Rs.320 B)Rs.350 C)Rs.370 D)Rs.480 E)None of these SOLUTION:Explanation : 100 % = 400 (100 * 4 = 400)120 % = 480 (120 * 4 = 480)Selling price = Rs.480/- Answer : D #### D QUESTION:Nirmala gains 10% by selling her bicycle for a certain price. If she sells it at 2 times the price, the percentage of profit will be : options: A)130% B)140% C)160% D)120% E)None of these SOLUTION:Explanation : Solution: Let C.P =Rs. x. then, S.P. = Rs. (110% of x) = Rs. 11x/10. New S.P. = Rs. (2*11x/10) =Rs. 22x/10. profit = Rs. (22x/10 - x) = Rs. 6x/5. .'. Profit% = (6x/5 *1/x * 100) = 120%. Answer : D #### D QUESTION:The sector of a circle has radius of 21 cm and central angle 130o. Find its perimeter? options: A)91.5 cm B)89.6 cm C)91.8 cm D)92.5 cm E)99.5 cm SOLUTION:Perimeter of the sector = length of the arc + 2(radius) = (130/360 * 2 * 22/7 * 21) + 2(21) = 47.6 + 42 = 89.6 cm Answer:B #### B QUESTION:The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? options: A)3.4 B)3.9 C)4.1 D)4.2 E)4.6 SOLUTION:Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. E #### E QUESTION:Workers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they? options: A)350 B)400 C)500 D)550 E)590 SOLUTION:N * 50 = (325000 - 300000) = 25000 N = 25000 / 50 = 500 C #### C QUESTION:A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge? options: A)Rs. 105 and Rs. 6 B)Rs. 216 and Rs. 12 C)Rs. 210 and Rs. 12 D)Rs. 210 and Rs. 6 E)None SOLUTION:Explanatory Answers Let half of the full basic fare be Rs. X. Therefore, full basic fare is Rs. 2X. Let the reservation charge be Rs. Y per ticket. Now, one full reservation ticket would cost 2X (basic fare) + Y (reservation charge) 2X + Y = 216 --- (1) The total basic fare for one half and one full ticket = X + 2X = 3X and the total reservation charge is 2Y. Hence, 3X + 2Y = 327 --- (2) Solving (1) and (2) we get, X = 105 and Y = 6 Hence, the full basic fare is 2X = Rs. 210 and the reservation charge is Y = Rs. 6 Answer D #### D QUESTION:There are two boxes,one containing 39 red balls & the other containing 26 green balls.you are allowed to move the balls b/w the boxes so that when you choose a box random & a ball at random from the chosen box,the probability of getting a red ball is maximized.this maximum probability is options: A)0.9 B)0.8 C)0.5 D)0.7 E)0.2 SOLUTION:Ans: Very interesting question. As we are allowed to move the balls, we keep only one red ball in first box and move all the remaining balls to the second box So fist box contains 1 redball, second box contains 38 red + 26 green = 64 balls Probability of choosing any box is 1/ 2. So probability of taking one red ball = 12×(1)+12(3864)≃0.8 Answer:B #### B QUESTION:At what time between 5.30 and 6 will the hands of a clock be at right angles? options: A)43 7/12 min. past 5. B)43 7/13 min. past 5. C)42 7/11 min. past 5. D)42 7/18 min. past 5. E)43 7/11 min. past 5. SOLUTION:At 5 o'clock, the hands are 25 min. spaces apart. To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces. 55 min. spaces are gained in 60 min. 40 min. spaces are gained in 60/55 x 40 min = 43 7/11 min. Required time = 43 7/11 min. past 5. Answer: E #### E QUESTION:The average marks of a class of 20 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students? options: A)44.28 B)54.28 C)34.28 D)64.28 E)74.28 SOLUTION:Sum of the marks for the class of 20 students = 20 * 40 = 800 Sum of the marks for the class of 50 students = 50 * 60 = 3000 Sum of the marks for the class of 70 students = 800 + 3000 = 3800 Average marks of all the students = 3800/70 = 54.28 ANSWER:B #### B QUESTION:If 40% of a number is 16, then the number is options: A)number is 60 B)number is 70 C)number is 90 D)number is 40 E)None of these SOLUTION:Solution: Let "a" be the number we seek. We get 40% × a = 16 2 × 40% × a = 2 × 16 = 32 80% × a = 32 10% × a = 32 : 8 = 4 100% × a = 4 × 10 = 40 a = 40 Answer D #### D QUESTION:A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of his total marks in English. How much does he score in English? options: A)55 B)66 C)77 D)44 E)None of these SOLUTION:Given student scores 55% marks in english in 8 papers of 100 marks each. so,his total marks are (55*800)/100 =>440 15% of his 440 marks is 440*(15/100)=>66 so,he scored 66 marks in english. ANSWER:B #### B QUESTION:The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 625 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units? options: A)140 B)99 C)100 D)72 E)12 SOLUTION:Given that the area of the square = 625 sq.units => Side of square = √625 = 25 units The radius of the circle = side of the square = 25 units Length of the rectangle = 2/5 * 25 = 10 units Given that breadth = 10 units Area of the rectangle = lb = 10 * 10 = 100 sq.units Answer: C #### C QUESTION:In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 16 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)? options: A)144 B)150 C)156 D)162 E)168 SOLUTION:Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 16 and the total number of coins is 9k = 144. The answer is A. #### A QUESTION:If 7 is 10 percent of 50 percent of a certain number, what is the number? options: A)150 B)217 C)100 D)90 E)140 SOLUTION:Using elimination method to pick the correct option it will be discovered that option E i.e 140 is the correct option because 50% of 140 is 70 and 10% of 70 is 7. ANSWER:E #### E QUESTION:If the sum of two numbers is 24 and the sum of their squares is 404, then the product of the numbers is options: A)40 B)44 C)80 D)86 E)90 SOLUTION:Sol. Let the numbers be x and y. Then, (x+y) = 24 and x2 + y2 = 404. Now, 2xy = (x+y)2 - (x2 + y2) = (24)2 - 404 = 576- 404 = 172 xy = 86. Answer D #### D QUESTION:During a clearance sale, a retailer discounted the original price of its TVs by 21% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay? options: A)40% B)45% C)55% D)60% E)63.5% SOLUTION:VERITAS PREPOFFICIAL SOLUTION: D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 75% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 75% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 75% sale price. Using fractions, that means they pay: 4/5*(3/4) of the original price, which nets to 3/5 of the original price, or 63.5%. E #### E QUESTION:A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed: options: A)60 birds B)72 birds C)30 birds D)80 birds E)20 birds SOLUTION:Let the total number of shots be x. Then, Shots fired by A =(5/8)x Shots fired by B =(3/8)x Killing shots by A =(1/3)of (5/8)x=(5/24)x Shots missed by B =(1/2) of (3/8)x =(3/16)x 3x/16= 27 or x =(27 x 16)/3= 144. Birds killed by A =(5x/24) =(5/24*144)= 30. Answer is C. #### C QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)210m B)240m C)963m D)874m E)578m SOLUTION:Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B)240m #### B QUESTION:X percents of the rooms are suits, Y percent of the rooms are painted light blue. Which of the following best represents the least percentage of the light blue painted suits? options: A)X-Y B)Y-X +100 C)100X-Y D)X+Y-100 E)100-XY SOLUTION:Using the simple formula 100 = X + Y - BOTH - > Here X = % of Suits , Y = % of light blue painted rooms and BOTH = % of suits painted in light blue colour So now, BOTH = X+Y -100 and now you can manipulate the value of X and Y to get the max and minimum values. Hence Answer D #### D QUESTION:A cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm. The total area of the wet surface is: options: A)120 m2 B)136 m2 C)128 m2 D)130 m2 E)134 m2 SOLUTION:Area of the wet surface = [2(lb + bh + lh) - lb] = 2(bh + lh) + lb = [2 (8 x 1.50 + 10 x 1.50) + 8 x 10] m2 = 134 m2. answer :E #### E QUESTION:A and B together can do a piece of work in 6 days and A alone can do it in 13 days. In how many days can B alone can do it? options: A)12 days B)15 days C)78/7 days D)21 days E)22/7 days SOLUTION:Explanation: A and B can do work 1/6 in 1 day A alone can do 1/13 work in 1 day B alone can do (1/6 -1/13) =7/78 work in 1 day => complete work can be done in 78/7 days by B Answer: Option C #### C QUESTION:From given equation find the value of x: 2x² + 9x − 5 options: A)−5 B)-4 C)-3 D)3 E)4 SOLUTION:That quadratic is factored as follows: 2x² + 9x − 5 = (2x − 1)(x + 5). Lesson 17. Now, it is easy to see that the second factor will be 0 when x = −5. As for the value of x that will make 2x − 1 = 0, we must solve that little equation. (Lesson 9.) We have: 2x = 1 x = 1 2 The solutions are: x = 1/2 or −5 A #### A QUESTION:If m=9^(x−1), then in terms of m, 3^(4x−6) must be which of the following? options: A)m/3 B)9m C)9m^2 D)m^2/3 E)m^2/9 SOLUTION:m = 9 ^ (X-1) m = 3 ^ (2x-2) m^2 = 3 ^ (4x-4) m^2/9 = 3 ^ (4x-6) Answer E #### E QUESTION:If P is a prime number greater than 10, what is the remainder when P^2 is divided by 2. options: A)Cannot be determined B)1 C)2 D)3 E)4 SOLUTION:take square of any prime number remainder will be 1 Ans B #### B QUESTION:If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ? options: A) x^2 - 9x B) x^2 - 9x + 20 C) x^2 - 2x + 3 D) x^2 + 2x + 1 E) x^2 + 5x + 6 SOLUTION:x^2-1 = 0 x= +1 or x = -1 if we substitute x= -1 in the equation x^2 +2x+1 = 1-2+1 = 0 D is also the answer #### D QUESTION:If t= 4p, where p is a prime number greater than 2, how many different positive even divisors does t have, including t ? options: A) Two B) Three C) Four D) Six E) Eight SOLUTION:t=4p since t = 4p thenevendivisors are: 4p/4p= 1 4p/2p= 2 4p/4= p 4p/2= 2p so the answer is (C) #### C QUESTION:A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? options: A) 18/79 B) 1/6 C) 1/25 D) 19/900 E) 1/900 SOLUTION:Everything is correct except that you assumed the letters can't be repeated. It can be repeated. AA BB CC AB, AC, BC, BA, CA, CB. Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900 Vehicles inspected within 3 hours = 60*3/9 = 19 P = 19/900 Ans:D #### D QUESTION:If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true? i. s=0 ii. u is not equal to v iii.u > v options: A)None B)I only C)II only D)III only E)II and III SOLUTION:Notice two things: 1. we are asked to find out which of the following MUST be true, not COULD be true and 2. s, u, and v are positive integers. Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. . Answer: A #### A QUESTION:If y exceeds x by 22%, then x is less than y by? options: A)18 2/8% B)18 8/3% C)18 2/61% D)76 2/3% E)17 2/3% SOLUTION:X=100 y=122 122------22 100-------? => 18 2/61% Answer:C #### C QUESTION:The average of first four prime numbers greater than 30 is? options: A)38 B)20 C)30 D)40 E)50 SOLUTION:31 + 37 + 41 + 43 = 152/4 = 38 ANSWER:A #### A QUESTION:A and B go around a circular track of length 900m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point? options: A)120 sec B)165 sec C)186 sec D)180 sec E)168 sec SOLUTION:Time taken to meet for the first time at the starting point = LCM { length of the track / speed of A , length of the track / speed of B} = LCM { 900/ (36 * 5/18) , 900/ (54 * 5 /18) } = LCM (90, 60) =180 sec. Answer:D #### D QUESTION:66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be : options: A)84 m B)88 m C)120 m D)137 m E)None SOLUTION:Sol. Let the length of the wire b h. Radius = 1/2 mm = 1/20 cm. Then, 22/7 * 1/20 * 1/20 * h = 66 ⇔ = [66 * 20 * 20 * 7 / 22] = 8400cm = 84 m. Answer A #### A QUESTION:9 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 48 cm height. What is the diameter of each sphere? options: A)4 cm B)6 cm C)8 cm D)10 cm E)12 cm SOLUTION:Volume of cylinder = pi*r^2*h Volume of a sphere = 4*pi*R^3 / 3 9*4*pi*R^3 / 3 = pi*r^2*h R^3 = r^2*h / 12 = 64 cm^3 R = 4 cm D = 8 cm The answer is C. #### C QUESTION:Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 45 more revolutions than gear P? options: A)45 B)80 C)90 D)100 E)120 SOLUTION:Gear Q makes 30 more revolutions each 60 seconds. The time to make 45 = 30*1.5 more revolutions is 60*1.5 = 90 seconds. The answer is C. #### C QUESTION:An inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2 meteres options: A)1200 B)2400 C)1400 D)2500 E)None of these SOLUTION:Explanation: It means that 0.08% of x = 2 =>(8/ 100×100×x)=2=>x=2×100×100/ 8=>x=2500 Option D #### D QUESTION:Shopkeeper rise price by 32% and gives successive discount of 10% and 15%. What is overall % gain or loss? options: A)0.98% B)4.98% C)3.95% D)6.98% E)7.98% SOLUTION:Let d initial price be 100 32 % rise now price = 132/100*100 = 132 10% discount Then price = 132 * 90/100 = 118.8 15 % discount Then price = 118.8 * 85/100 = 100.98 So Gain = 100.98 - 100 = 0.98 Gain % = Gain * 100 /CP ==> 0.98* 100 /100 = 0.98% ANSWER:A #### A QUESTION:A man on tour travels first 120 km at 60 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 280 km of tour. options: A)70.00 km/hr B)71.11 km/hr C)72.11 km/hr D)73.11 km/hr E)None of these SOLUTION:Explanation: We know Time = Distance/speed So total time taken = (120/60+160/80)=4hours Time taken for 280 Km = 280/4=70.km/hr Option A #### A QUESTION:A boy has five trousers and 15 shirts. In how many different ways can he select a trouser and a shirt? options: A)75 ways B)87 ways C)66 ways D)108 ways E)21 ways SOLUTION:Explanation: The boy can select one trouser in five ways. The boy can select one shirt in 15 ways. The number of ways in which he can select one trouser and one shirt is 5 * 15 = 75 ways. Answer: A #### A QUESTION:Set A contains three different positive odd integers and three different positive even integers. Set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even? options: A)3/5 B)2/5 C)1/2 D)4/5 E)19/25 SOLUTION:There can be an odd product only if both integers are odd. P(odd product) = 1/2*2/5 = 1/5 P(even product) = 1 - 1/5 = 4/5 The answer is D. #### D QUESTION:If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area? options: A)230 cm^2 B)240 cm^2 C)250 cm^2 D)260 cm^2 E)270 cm^2 SOLUTION:The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm. Area of the triangle = 1/2 * 36 * 15 = 270 cm^2 Answer: E #### E QUESTION:A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? options: A)109% B)160% C)100% D)600% E)108% SOLUTION:MP = 100 CP = 75 SP = 150 ------ 75 ---- 75 100 ---- ? => 100% Answer:C #### C <<<Examples ends QUESTION:Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time? options: A)17 1/9 B)17 1/3 C)17 1/7 D)17 1/9 E)17 1/1 SOLUTION:1/20 + 1/30 - 1/40 = 7/120 120/7 = 17 1/7 Answer: C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 11 hours longer than the first half, how many hours did it take the runner to run the second half? options: A)14 B)15 C)18 D)22 E)33 SOLUTION:The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2. The time T2 to run the second half must be twice the time T1 to run the first half. T2 = 2*T1 = T1+11 T1 = 11 and so T2 = 22. The answer is D. #### D QUESTION:If 7 ministers are to be seated at a round table conference, then how many different ways can they be seated? options: A)24 B)60 C)720 D)520 E)180 SOLUTION:Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle. so its (7-1)! = 6! = 720=C #### C QUESTION:The area of a square is 625 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is thrice the side of the square and breadth is 20 cm less than the side of the square. options: A)5 : 12 B)5 : 13 C)2:9 D)1:15 E)1:5 SOLUTION:Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm. a2 = 625 a = 25 L = 3a and b = a - 20 b : l = a - 20 : 3a = 5 : 75 = 1:15 Answer: D #### D QUESTION:There are 9 books on a shelf that consist of 3 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book? options: A)95 B)103 C)111 D)119 E)127 SOLUTION:The total number of ways to select 4 books is 9C4 = 126 The number of ways which do not include any paperbacks is 6C4 = 15 The number of combinations with at least one paperback is 126-15 = 111 The answer is C. #### C QUESTION:After decreasing 50% in the price of an article costs Rs.620. Find the actual cost of an article? options: A)2777 B)2987 C)1200 D)1240 E)1671 SOLUTION:CP* (50/100) = 620 CP= 12.4 * 100 => CP = 1240 Answer: D #### D QUESTION:If the probability W of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period? options: A)8/125 B)2/25 C)5/16 D)8/25 E)3/4 SOLUTION:5C3 (1/2)^3(1/2)^2 = (5 * 4 * 3!)/2!3! * 1/32 W= 5/16 Answer - C #### C QUESTION:Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 20 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent? options: A)20% B)80% C)100% D)180% E)200% SOLUTION:We can use fractional equivalents here to solve the problem 80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears 10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours Now we come to productivity Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour Hence the productivity is double with the assistant i.e. the increase in productivity is 180% D #### D QUESTION:A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 210 sq. feet, how many feet of fencing will be required? options: A)34 B)41 C)68 D)88 E)None SOLUTION:EXPLANATION We have: l = 20 ft and lb = 210 sq. ft. So, b = 10.5 ft. Length of fencing = (l + 2b) = (20 + 21) ft = 41 ft. Answer B #### B QUESTION:Each shelf of a bookcase contained 11 books. If the librarian took out 30 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 5 books, how many shelves does the bookcase have? options: A)5 B)6 C)7 D)8 E)9 SOLUTION:Let x be the number of shelves. 11x - 30 = 7(x-1) + 5 4x = 28 x = 7 The answer is C. #### C QUESTION:A red ant is sitting on one side of a table (point X) and a black ant is sitting on the opposite side of the table (point Y). Now both of them decides to exchange their places and starts crawling. On the way, both of the ants meet and after that, it takes 20 seconds for the Red ant to move to point Y and it takes 5 seconds for the Black ant to reach point X. Find out the total time taken by the Red and the Black ant to make the journey. options: A)30 and 15 seconds B)10 and 15 seconds C)20 and 15 seconds D)25 and 15 seconds E)5 and 15 seconds SOLUTION:Solution: Let the speed of red ant be R. Speed of Black ant be B. Time at which they cross their paths be T. Now we will apply the basic formula of distance Distance = Speed * Time The Red ant travels R * T distance before meeting and R * 20 after meeting. The Black ant travels B * T distance before meeting and B * 5 after meeting. Now as per the question, The distance traveled by red ant before they both meet will be equal to the distance covered by black ant after they meet. We can say the same for the vice versa case as well. Thus R * T = B * 5 and B * T = R * 20 Using both the quations T = 10 Thus the red ant will require 10 + 20 = 30 seconds to travel the distance. And the black ant will take 10 + 5 = 15 seconds to travel the distance. Answer A #### A QUESTION:The average height of 30 students in a class was calculated as 177 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm. What was the actual average height of the students in the class? options: A)176.5 cm B)175.5 cm C)174.5 cm D)173.5 cm E)172.5 cm SOLUTION:The total height was 45 cm too much. The average height should be reduced by 45 cm/30 = 1.5 cm The answer is B. #### B QUESTION:HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is? options: A)36 B)66 C)132 D)264 E)152 SOLUTION:12 * 396 = 36 * x x = 132 ANSWER:C #### C QUESTION:A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? options: A)7 1/2 years B)20 years C)15 years D)38 years E)30 years SOLUTION:100 ---- 100 --- 10 100 --- 10 -------------------- 300 ---- 20 years ANSWER:B #### B QUESTION:If each side of the square is increased by 25% find the percentage change in its area? options: A)89.45% B)56.25% C)89.98% D)54.48% E)45.0% SOLUTION:let each side of the square be a. then area =a^2 new side=125a/100=5a/4 new area=(5a/4)^2=25a^2/16 increase in area=(25a^2/16-a^2)=9a^2/16 increased %=(9a^2/16*1/a^2*100)=56.25% Answer is(B) #### B QUESTION:A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg? options: A)s.50 B)s.46 C)s.49 D)s.41 E)s.42 SOLUTION:1000*(25/100) = 250 ---- 5 ? ---- 1 => Rs.50 Answer: A #### A QUESTION:The average weight of 10 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? options: A)100 kg B)102.5 kg C)85 kg D)Data inadequate E)None of these SOLUTION:Explanation: Total weight increased = (10 x 3.5) kg = 35 kg. Weight of new person = (65 + 35) kg = 100 kg. Answer: A #### A QUESTION:By selling 33 meters of cloth , one gains the selling price of 11 metres . Find the gain percent . options: A)50 B)45 C)40 D)60 E)55 SOLUTION:(Selling Price of 33m)-(Cost Price of 33m)=Gain=Selling Price of 11m Selling Price of 22m = Cost Price of 33m Let Cost Price of each meter be $1 , Then, Cost Price of 22m= $22, Selling Price of 22m=$33. Gain%=[(11/22)*100]%=50% Answer A) 50. #### A QUESTION:If six persons sit in a row, then the probability that three particular persons are always together is -. options: A)1/5 B)1/7 C)1/9 D)1/2 E)2/7 SOLUTION:3!4! Required probability = 3!4!/6! = 1/5 ANSWER A #### A QUESTION:A man can row upstream at 8kmph and downstream at 13 kmph. The speed of the stream is options: A)2.5 km/hr B)4.2 km/hr C)5 km/hr D)10.5 km/hr E)None SOLUTION:Sol. Speed of stream = 1/2(13 -8) kmph = 2.5 kmph. Answer A #### A QUESTION:A student is ranked 12th from right and 6th from left. How many students are there in totality ? options: A)17 B)19 C)20 D)21 E)22 SOLUTION:From right 12 , From left 6 Total = 12+6-1 = 17 ANSWER:B #### B QUESTION:Albert borrowed a total of $ 6000 from Brian and Milton. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years? options: A)491 B)481 C)471 D)441 E)445 SOLUTION:Let x be the amount borrowed form Brian. So amount borrowed form Milton = 6000-x. 1494 = 21/100x + 27/100(6000-x) =>x = 2100. Interest paid = 3*7/100*2100 = 441. D #### D QUESTION:How many of the positive factors of 42 , 104 and how many common factors are there in numbers? options: A)4 B)2 C)3 D)5 E)1 SOLUTION:factors of 42 - 1,2,3,6,7,14,21,42 factors of 104 - 1,2,4,8,13,26,52,104 Comparing both, we have two common factors of 40 and 104- 1,2, Answer(B) #### B QUESTION:There are 17 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season? options: A)980 B)1150 C)1360 D)1540 E)1720 SOLUTION:The number of ways to choose two teams is 17C2 = 17*16/2 = 136 The total number of games in the season is 10*136 = 1360. The answer is C. #### C QUESTION:John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today? options: A)8 years B)10 years C)12 years D)14 years E)15 years SOLUTION:Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j) and Rupesh + 6 = | (Ravi + 6) ...(ii) Solving both the equations we get, Ravi = 12 years. C #### C QUESTION:one kilo gram coffee is Rs. 126 and Rs. 135 are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the 3rd variety per kilo gram is? options: A)150 B)133 C)175.5 D)178 E)190 SOLUTION:Since first and second varieties are mixed in equal proportions. So, their average price = Rs. 126 + 135 = Rs. 130.50 2 So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. By the rule of alligation, we have: Cost of 1 kg of 1st kindCost of 1 kg tea of 2nd kind Rs. 130.50 Mean Price Rs. 153 Rs. x (x - 153) 22.50 x - 153 = 1 22.50 x - 153 = 22.50 x = 175.50 C #### C QUESTION:The average of six number is 3.95. The average of two of them is 3.8, while the average of the other two is 3.85. what is the average of the remaining two number ? options: A)4.5 B)4.2 C)4.7 D)4.8 E)None of these SOLUTION:solution: Sum of the remaining two numbers = (3.95 × 6) - [(3.8 × 2) + (3.85 ×2)] =23.70 -(7.6 + 7.7) = 23.70 - 15.3 = 8.4. ∴ Required average =8.4/2 = 4.2 Answer B #### B QUESTION:Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 19 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? options: A)565 B)444 C)676 D)420 E)663 SOLUTION:1h ----- 3 ? ------ 60 12 h RS = 16 + 19 = 35 T = 12 D = 35 * 12 =420 Answer: D #### D QUESTION:There are six leopards and one sheep. Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s). If we leave them for some time then how many sheep and leopard will be there , when we come back ? options: A)4 leopard and one sheep B)5 leopard and one sheep C)6 leopard and one sheep D)7 leopard and one sheep E)None SOLUTION:Solution: 5 leopard and one sheep since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this. Answer B #### B QUESTION:A plane flying north at 500 kmph passes over a city at 12 noon. A plane flying east at the same attitude passes over the same city at 12.30 pm. The plane is flying east at 400 kmph. To the nearest hundred km, how far apart are the two planes at 2 pm? options: A)600 km B)1000 km C)1100 km D)1200 km E)1300 km SOLUTION:The plane flying north would have traveled for 2 hours at 2 PM. It travels at 500 kmph. Hence, the plane flying north would have covered 1000 kms from the city at 2 PM. The plane flying east would have traveled for 1.5 hours at 2 PM. It travels at 400 kmph. Hence, the plane flying east would have covered 1.5*400 = 600 kms from the city at 2 PM. The two planes are flying at right angles to each other. The shortest distance between the two planes is the length of the hypotenuse of the right triangle whose legs are the distances covered by the two planes. Hence, distance = 1000square + 200 square = 1166 km The nearest 100 km distance between the two planes = 1200 kms. Answer D #### D QUESTION:What is the greatest possible length that can be used to measure exactly the following Lengths 7m, 3m 85cm, 12m 95cm? options: A)25 cms B)30 cms C)35 cms D)38 cms E)45 cms SOLUTION:HCF of 7m, 3m 85cm, 12m 95cm is 35 cms. ANSWER:C #### C QUESTION:S is a set containing 8 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true? options: A) The median of S is prime. B) The median of T is prime C) The median of S is equal to the median of T. D) The sum of the terms in S is prime. E) The sum of the terms in T is prime. SOLUTION:Here is my explanation. The question states:S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true? (A) The median of S is prime. Thismust be true. If there are an odd number of members of a set, then the median is a member of the set: it's the middle number, when all the numbers are ranked from smallest to biggest. Every number in S is a positive odd prime, so the median is one of them, and is prime. (B) The median of T is prime. Thismay or may not be true. If a set has an even number of members, the median is average of the two numbers in the middle, when ranked from smallest to biggest. The average of two odd numberscould beeven (average of 71 and 73 is 72), and hence not prime, or itcould beodd (the average of 71 and 79 is 75). For particularly well chosen odd numbers, the average can be not only odd but also prime -- for example, the average of 89 and 113 is 101, another prime number. If the two middle numbers of T were 89 and 113, the median would be 101, a prime number. (C) The median of S is equal to the median of T. Under most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to have an average of that number that was dropped (for example, if the two numbers were 89 and 113), then the medians would be equal. In other words, the three middle numbers of S would have to be {. . ., 89, 101, 133, . . .}, and when 101 is dropped in going to T, the median of two would be the average of 89113, which happens to be 101. It's an exceptional case, but itcouldbe true. (D) The sum of the terms in S is prime. Thismay or may not be true. The sum of 9 odd numbermustbe an odd number. That odd numbercould beprime. For example, the sum of the first nine odd prime numbers {3, 5, 11, 13, 17, 19, 23, 29} is 127, which is prime. If you drop 3 and include the next prime, 31, the set {5, 11, 13, 17, 19, 23, 29, 31} has a sum of 155, which is clearly not prime. (E) The sum of the terms in T is prime. Thismust be false. The sum of eight odd numbers must be an even number. Only 2 is prime, and all other even numbers are not. Therefore, the sum of eight odd prime numbers will be an even number bigger than two, and absolutely cannot be prime. C #### C QUESTION:The average weight of a group of 30 friends increases by 3 kg when the weight of their 3 football coaches was added. If average weight of the group after including the weight of the 3 football coach is 33 kg, what is the average weight of their football coaches ? options: A)31 kg B)63 kg C)61 kg D)62 kg E)91 kg SOLUTION:let c=coach's avg. weight original total weight=(30 friends)(30 kg avge)=900kg (900+3c)/(30+3)=33 kg avg. c=63 kg Answer B #### B QUESTION:Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit? options: A)10000 B)12000 C)13000 D)14000 E)30000 SOLUTION:SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000 E #### E QUESTION:In expressing a length of 25.461 km as nearly as possible with the three significant digits, find the percentage error options: A)0.353% B)0.153% C)0.035% D)0.015% E)None of these SOLUTION:Explanation: Error = (25.5 - 25.461) = 0.039 Required percentage = 0.039/ 25.461×100=0.153 Option B #### B QUESTION:A computer store offers employees a 20% discount off the retail price. If the store purchased a computer from the manufacturer for $1000 dollars and marked up the price 20% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (20% off retail price) as opposed to the final retail price. options: A)$1,000 B)$960 C)$240 D)$200 E)$150 SOLUTION:Cost price=1000 Profit=20% =20% of 1000=200 selling price=CP+ Profit SP=1200 a Discount of 20% to employees means 20% off on 1200 so 20% of 1200= 240 so a employee thinks he saved 240.. Answer: C #### C QUESTION:Souju's age is 115% of what it was 10 years ago, but 83 1/3% of what it will be after 10 years. What is her present age? options: A)56 years B)72 years C)56 years D)66 years E)76 years SOLUTION:Let the age before 10 years =x. Then, 115x/100=x+10 ⇒115x=100x+1000 ⇒x=1000/15=66 Present age =x+10=66+10=76 ANSWER:E #### E QUESTION:What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x options: A)35678 B)73205 C)75653 D)86554 E)87565 SOLUTION:(B) 5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205 #### B QUESTION:At what rate percent on simple interest will a sum of money double itself in 20 years? options: A)2% B)6% C)3% D)4% E)5% SOLUTION:P = (P*20*R)/100 R = 5% ANSWER:E #### E QUESTION:Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 9. What is the value of x? options: A)20 B)60 C)100 D)120 E)150 SOLUTION:y = 0.5*0.5*x = x/4 y%*x = 9 (y/100)*x = 9 (x/400)*x = 9 x^2 = 9*400 x = 60 The answer is B. #### B QUESTION:Ravi's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the Ravi's average score on the 5 tests to be 80? options: A) 80 B) 82 C) 84 D) 86 E) 88 SOLUTION:E. 88 Ravi must score at least an 80 for sure. If he scores an 8, then he will need to score 2 pots for each of the 4 other tests tomake upthe difference. They each were at 78 (at least the average is, but this is a small point and doesn't matter to the answer). So 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average, so 80+8 = 88. #### E QUESTION:A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be? options: A)15 m, 12 m B)15 m, 11 m C)15 m, 20 m D)15 m, 10 m E)15 m, 11 m SOLUTION:lb = 150 2(l + b) = 50 => l + b = 25 l – b = 5 l = 15 b = 10 D #### D QUESTION:Evaluate 25% of 450 + 45% of 250 options: A)225 B)242 C)252 D)262 E)272 SOLUTION:Explanation: = (25/100) * 450 + (45/100) * 250 = 225 Option A #### A QUESTION:The product of the prime numbers between 0 and 20 is closest to... options: A)10^5 B)10^6 C)10^7 D)10^8 E)10^9 SOLUTION:Write out the primes 1 - 20 2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 Round the numbers off in multiples of 5. Try to alternate rounding up and down 5 x 5 x 5 x 5 x 10 x 10 x 20 x 20 25 x 25 x 10 x 10 x 20 x 20 pull out 10 from each number 10^6 (2.5 x 2.5 x 2 x 2) 10^6 (5 x 4) 10^7 (2) round off the 2. answer is C #### C QUESTION:Sara's mother is 6 times older than Sara. Next year, however, she will be only 5 times older than her daughter. How old is Sara's mother. options: A)24 years B)25 years C)26 years D)27 years E)28 years SOLUTION:At the present, Sara's age is x. Sara's mother's age is y=6x. Next year, Sara's age will be x+1. Sara's mother's age will be y+1=5(x+1). From the two equations, we can calculate Sara's age: y=6x y+1=5 (x+1) 6x+1=5x+5 6x-5x=5-1 x=4 If Sara is currently 4 years old, and her mother is 6 times older, then her age is 6x=6×4=24. ANSWER: A #### A QUESTION:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points R is in the same quadrant as the fourth vertex of the square? options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5) SOLUTION:The question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points R is in the same quadrant as the fourth vertex of the square? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E QUESTION:The following sets each have a mean of 10 and the standard deviations are given in variable form. Set I = {7, 8, 9, 11, 12, 13}, standard deviation = P Set II = {6, 6, 6, 14, 14, 14}, standard deviation = Q Set III = {10, 10, 10, 10, 10, 10}, standard deviation = R Rank these three standard deviations from least to greatest. options: A)P, Q, R B)P, R, Q C)Q, P, R D)Q, R, P E)R, P, Q SOLUTION:SD is minimum when the terms are closer to the mean. In set 3, we have all terms equal to mean. hence, its SD is 0.(The Lowest) Comparing Set 1 and Set 2, Set 1 has terms more closer to mean than set 3. hence, Set 3 Sd is the highest. So, Answer is E #### E QUESTION:A crate of apples contains 1 bruised apple for every 25 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate? options: A)270 B)360 C)480 D)600 E)400 SOLUTION:as given 3 out of every 4 bruised apple is not fit to sell or, 75% of the bruised apples are not fit to sell. as per the question 12 are not fit to sell or, 0.75x=12 x=1200/75=16 thus total number of bruised apples =16 total number of apples =25*16=400 Answer: E #### E QUESTION:If the wheel is 15 cm then the number of revolutions to cover a distance of 1056 cm is? options: A)18 B)11.2 C)14 D)12 E)91 SOLUTION:2 * 22/7 * 15 * x = 1056 => x = 11.2 Answer: B #### B QUESTION:Let the number which when multiplied by 11 is increased by 300. options: A)14 B)20 C)26 D)28 E)30 SOLUTION:Solution Let the number be x . Then, 11x - x = 300 ‹=›10x = 300 x ‹=› 30. Answer E #### E QUESTION:If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 72? options: A)24 B)36 C)12 D)18 E)16 SOLUTION:The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8. The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5. 72=2*3*3*2*2 is divisible by 12. therefore the greatest common divisor is 12 C #### C QUESTION:A fruit salad mixture consists of apples, peaches, and grapes. There are 3 times as many pounds of apples as grapes and 2.5 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 39 pounds per fruit, how many more pounds of apples than grapes does the mixture have? options: A)5 B)12 C)19 D)36 E)50 SOLUTION:A+P+G= 39*3 A=3G P=2.5G 3G+2.5G+G= 39*3 G=39*3/6.5= 18 A= 6*3=54 Difference = 36 'D' is the answer #### D QUESTION:The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder? options: A)308 sq cm B)220 sq cm C)440 sq cm D)132 sq cm E)138 sq cm SOLUTION:r = 7 h = 3 2πr(h + r) = 2 * 22/7 * 7(10) = 440 ANSWER:C #### C QUESTION:Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? options: A)7 hours 15 minutes B)8 hours 15 minutes C)7 hours 30 minutes D)8 hours 30 minutes E)8 HOURS 15 MINUTES SOLUTION:Number of pages typed by Ravi in 1 hour = 32/6 = 16/3 . Number of pages typed by Kumar in 1 hour = 40/5 = 8. Number of pages typed by both in 1 hour = ( 16/3 + 8 ) = 40/3 . Therefore Time taken by both to type 110 pages = ( 110 x 3/40 ) hours = 8 hours 15 minutes. ANSWER : E #### E QUESTION:If the average (arithmetic mean) of 5 positive temperatures is z degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be: options: A)6z B)4z C)5z/3 D)3z/2 E)3z/5 SOLUTION:The sum of three greatest should be more than sum of two lowest. The total sum is; 5z A. 6z; 6z is more than 5z. Not possible. B. 4z; 5z-4z=z(Possible) C. 5z/3; 10z/3; 10z/3 > 5z/3. Not possible D. 3z/2; 7z/2; 7z/2 > 3z/2. Not possible E. 3z/5; 22z/5; 22z/5 > 3z/5. Not possible. Ans:B #### B QUESTION:If $0.80 is the commission for sales of $2,000, what percent of the sales amount is the commission? options: A)4% B)0.4% C)0.04% D)0.004% E)0.0004% SOLUTION:% of sales amount of commission = (Commission/Total Value) *100 = (0.8/2000) * 100 = 0.04% The answer is C. #### C QUESTION:A jeep takes 7 hours to cover a distance of 420 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? options: A)48 Kmph B)52 Kmph C)40 Kmph D)63 Kmph E)65 Kmph SOLUTION:Time = 7 Distance = 420 3/2 of 7 hours = 7 * 3/2 = 10.5 Hours Required speed = 420/10.5 = 40 Kmph C) #### C QUESTION:Tom read a book containing 1000 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 15 pages a day more, how many days did Tom spend reading the book? options: A)20 B)18 C)16 D)15 E)15.39 SOLUTION:Actually u can set up 2 equation P--stands for the pages D--stands for the days 1) P*D=480 (we want to find the Days, soP=480/D) 2) (P+15)(D-5)=1000=> PD-5P+15D-75=1000 as the 1) stated u can put 1) into 2) => 1000-5P+15D-75=1000 => 15D-5P=75 put the bold one into it => 15D-5(480/D)=75the we get the final equation 16D^2-2400=80D (divide 16) => D^2-5D-160=0 so D=15.39days. Ans: (E) #### E QUESTION:What is the difference between the local values of 4 in the number 54404? options: A)2992 B)3996 C)2877 D)2077 E)1211 SOLUTION:Explanation: 4000 – 4 = 3996 Answer:B #### B QUESTION:The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group? options: A)87 B)67 C)23 D)75 E)25 SOLUTION:Let the initial number of members in the group be n. Initial total weight of all the members in the group = n(48) From the data, 48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23 Therefore there were 23 members in the group initially. Answer: C #### C QUESTION:The average temperature for Wednesday, Thursday and Friday was 40oC. The average for Thursday, Friday and Saturday was 41oC. If temperature on Saturday was 42oC, what was the temperature on Wednesday? options: A)39oC B)44oC C)38oC D)41oC E)None SOLUTION:Solution: Average temperature for Wednesday, Thursday and Friday = 40oC Total temperature = 3*40 = 120oC Average temperature for Thursday, Friday and Saturday = 41oC Total temperature = 41*3 = 123oC Temperature on Saturday = 42oC Now, (Thursday + Friday + Saturday) - (Wednesday + Thursday + Friday) = 123-120; Saturday - Wednesday = 3 Wednesday = 42-3 = 39oC. Answer: Option A #### A QUESTION:A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent E of the list price is the lowest possible sale price? options: A)20 B)25 C)30 D)40 E)50 SOLUTION:Let the list price be 2x for min sale price, the first discount given should be 50%, 2x becomes x here now, during summer sale additional 20% off is given ie sale price becomes 0.8x it is given lise price is $80 => 2x = 80 => x = 40 and 0.8x = 32 so lowest sale price is 32, which E is 40% of 80 hence, D is the answer #### D QUESTION:The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be: options: A)5:2 B)7:3 C)9:2 D)13:4 E)3:4 SOLUTION:Let the age of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] 3x + 20 = 2x + 40 => x = 20. Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3 ANSWER:B #### B QUESTION:Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible? options: A)10 B)21 C)210 D)420 E)1,260 SOLUTION:First Select 5 from 7 contestants and then select top 3 from those 5 = 7C5*5C3 = 42 * 5 = 210 ANS:C #### C QUESTION:Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3? options: A)17 kmph B)50 kmph C)18 kmph D)17 kmph E)11 kmph SOLUTION:Let the distances between city A to B and B to C be 2x km and 3x km respectively. Total time taken to cover from A to C = (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph. Answer:B #### B <<<Examples ends QUESTION:Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 6. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased? options: A)3, 8, 24 B)7, 9, 17 C)6, 9, 12 D)5, 15, 18 E)9, 10, 13 SOLUTION:I didnt get your point on eliminating A. The number of stamps only one purchased was divisible by 6.Could that not be Cecilia with 9 stamps. I choose this and marked A. #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A train running at the speed of 54 km/hr crosses a pole in 9 sec. What is the length of the train? options: A)135 m B)786 m C)566 m D)546 m E)445 m SOLUTION:Speed = 54 * 5/18 = 15 m/sec Length of the train = speed * time = 15 * 9 = 135 m Answer: A #### A QUESTION:3, 5, 7, 11, 13, 17, 19, ____ options: A)25 B)36 C)23 D)49 E)27 SOLUTION:The sequence is a series of prime numbers, 3, 5, 7, 11, 13, 17, 19, 23.... Answer : C. #### C QUESTION:Which of the following is non-negative number? options: A)(a-0.9)(a-1) B)(a+1)(a-1) C)(a+0.9)(a+1) D)(a-0.6)(a-0.6) E)a(a+1) SOLUTION:5-sec approach: D. (a-0.6)(a-0.6) = (a-0.6)^2. The square of a number is always non-negative. Answer: D. #### D QUESTION:If x is divisible by 2, 7, and 11, which of the following must also be a divisor of x? options: A)308 B)154 C)70 D)44 E)21 SOLUTION:If Multiple divisors of any integers are mentioned just take the LCM of all the divisors and the integer will be divisible by that. LCM of 2,7,11= 154 Hence x must be divisible by 154 Hence B #### B QUESTION:In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is: options: A)4884 B)5340 C)5342 D)5345 E)5356 SOLUTION:Divisor = (5 * 44) = 220 = 10 * Quotient = Divisor => Quotient = 220/10 = 22 Dividend = (Divisor * Quotient) + Remainder Dividend = (220 * 22) + 44 = 4884. A #### A QUESTION:Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 1500. What is their H.C.F.? options: A)5 B)15 C)25 D)35 E)45 SOLUTION:Let the numbers be 3x, 4x and 5x. Then, their L.C.M. = 60x 60x = 1500 x = 25 The numbers are (3 x 25), (4 x 25) and (5 x 25). The H.C.F. is 25. The answer is C. #### C QUESTION:When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha? options: A)40 B)41 C)42 D)43 E)45 SOLUTION:Let the age of Usha is 3x then Nisha is x and Asha is 25 Also Usha 34, Nisha y, and Asha 2y. We know that 3x - 34 = x - 2y = 25 - 2y Solving above three equations we get x = 9, y = 16 Their ages are 34, 16, 32. whose sum = 82. So after 18 years their ages will be equal to 100. So Usha age is 34 + 6 = 40 Answer:A #### A QUESTION:A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 14 men leave the bus and seven women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ? options: A)63 B)30 C)36 D)45 E)46 SOLUTION:Explanation: Originally, let number of women = x. Then, number of men = 2x. So, in city Y, we have : (2x - 14) = (x + 7) or x = 21. Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 63. Answer: A #### A QUESTION:If n is an integer, which of the following CANNOT be a factor of 3n+4? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:3n+4=3(n+1)+1 cannot be a multiple of 3, it's 1 more than multiple of 3: ... 4, 7, 10, 13, 16, ... Hence it cannot be a multiple of 2*3=6 as well. Answer: C. #### C QUESTION:If p/q =4/5, then the value of 1/7 + {(2q - p) / (2q + p)} is ? options: A)4 / 7 B)34 C)1 D)2 E)3 SOLUTION:Answer Given Exp. = 4 / 7 + {(2q - p) / (2q + p)} Dividing numerator as well as denominator by q, Exp = 1/7 + {2-p/q) / (2 + p/q)} = 1/7 + {(2 - 4/5) / (2 + 4/5)} = 1/7 + 6/14 = 1/7 + 3/7 =4/7 Correct Option: A #### A QUESTION:A classroom has equal number of boys and girls. SEVEN girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially? options: A)16 B)24 C)32 D)28 E)54 SOLUTION:after 7 girls left remaining 7 girls now boys 14 are twice as many as remaining girls. initially boys=14 and girls=14. ANSWER:D #### D QUESTION:If 1 persons can do 1 times of a particular work in 1 day, then, 7 persons can do 7 times of that work in ? options: A)3 days B)1 day C)9 days D)11 days E)15 days SOLUTION:That is, 1 person can do one time of the work in 1 day. Therefore, 7 persons can do 7 times work in the same 1 day itself. Option 'B' #### B QUESTION:Four milkmen rented a pasture, A grazed 18 cows for 4 months; B 25 cows for 2 months, C 28 cows for 5 months and D 21 cows for 3 months. If A's share of rent is Rs.360, the total rent of the field is : options: A)Rs.1500 B)Rs.1600 C)Rs.1625 D)Rs.1650 E)None SOLUTION:Explanation: Ratio of rents =(18×4:25×2:28×5:21×3)(18×4:25×2:28×5:21×3) =72:50:140:63 Let total rent = Rs.x Then, A's share = Rs.(x×72/325)= Rs.(72x/325) 72x/325=360 or x = 325×360/72=1625 Correct Option: C #### C QUESTION:In an exam, Dibi scored 25 percent, Balan scored 38 percent and Cristen 23 percent. The maximum score awarded in the exam is 1200. Find the average mark scored by all the three boys? options: A)322 B)342 C)344 D)328 E)320 SOLUTION:Average mark scored by all the three boys = [25/100 (1200) +38 /100 (1200) + 23/100 (1200)] / 3 300+456+276= 344 Answer: C #### C QUESTION:A computer wholesaler sells 11 different computers and each is priced differently. If the wholesaler chooses three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display? options: A)15/56 B)3/28 C)1/28 D)1/56 E)3/55 SOLUTION:Since, two of the choices are prefixed, we are free to choose 1 from the rest of the 9 avilable. so 9C1 is the numerator. Total no of ways we can choose 3 from 11 is 11c3, which is the denominator. So, the probability: 9c1/11c3= 3/28 ans is E. #### E QUESTION:You have been given a physical balance and 7 weights of 40, 42, 36, 33, 47, 52 and 67 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 169 kgs. options: A)163 B)166 C)162 D)164 E)165 SOLUTION:67 + 52 + 47 = 166 Answer: E #### E QUESTION:If the discount on Rs. 498 at 5% simple interest is Rs.18, when is the sum due? options: A)8 months B)11 months C)10 months D)9 months E)12 months SOLUTION:Explanation : F = Rs. 498 TD = Rs. 18 PW = F - TD = 498 - 18 = Rs. 480 R = 5% TD = (PW × TR)/100 ⇒ 18 = (480 × T × 5)/100 ⇒ 18 = 24 × T ⇒ T = 18/24 = 3/4 years = (12×3)/4 months = 9 months Answer : Option D #### D QUESTION:A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 120 km downstream? options: A)60/18 B)30/29 C)60/12 D)60/13 E)30/82 SOLUTION:Speed downstream = 20 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 120/26 = 60/13 hours. Answer:D #### D QUESTION:In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 8,000 have been vaccinated against both, how many have been vaccinated only against rubella? options: A)2,5000 B)7,500 C)10,000 D)15,000 E)16,000 SOLUTION:Use a single variable as far as possible. Number vaccinated only against mumps = x Number vaccinated against both = 2x = 8000 (so x = 4000) Then, number vaccinated against mumps (including both) = x + 2x = 3x Number vaccinated against rubella = 2*3x = 6x Then, number vaccinated against only rubella = 6x - 2x = 4x = 4*4000 = 16,000 Answer (E) #### E QUESTION:The sum of the first 50 positive even integers is 2,000. What is the sum of the odd integers from 101 to 200, inclusive? options: A) 5,050 B) 7,500 C) 8,050 D) 15,000 E) 19,600 SOLUTION:101+103+.......199 If we remove 100 from each of these it will be sum of 1st 100 odd numbers. so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050 Sum of 1st 50 positive even integers = 2000 sum of 1st 100 odd numbers = 5050 - 2000 = 3050 so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) = 5000 + 3050 =8050 C is the answer. #### C QUESTION:In the xy-coordinate system, what is the slope of the line that goes through point (2, 4) and is equidistant from the two points P = (9, 3) and Q = (5, 9)? options: A)0.1 B)0.2 C)0.3 D)0.4 E)0.5 SOLUTION:First, get the middle coordinate between (9,3) and (5,9). x = 9 + (5-9)/2 = 7 y = 3 + (9-3)/2 = 6 Second, get the slope of (7,6) and (2,4). m = 6-4 / 7-2 = 2/5 = 0.4 Answer: D #### D QUESTION:In how many Q ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password? options: A)720 B)864 C)900 D)936 E)1,296 SOLUTION:Total number of four letter passwords = 6*6*6*6= 1296 ------(1) Total number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2) therefore required value Q= (1)-(2)= 1296-360=936.D #### D QUESTION:The total of company C's assets in 1994 was 200% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994: options: A)7N B)8N C)9N D)12N E)15N SOLUTION:Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets. In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992: $100 + 4x$100 = $100 + $400 =$500 In 1994, the total assets were 200% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993: $500 +2x$500 = $500 + $1000 =$1500 This is 15 times the 1992 number, so the correct answer is 15N. #### E QUESTION:The average of first 13 even numbers is? options: A)10 B)11 C)12 D)13 E)14 SOLUTION:Sum of 13 even numbers = 13 * 14 = 110 Average = 182/13 = 14 ANSWER:E #### E QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1400, then what is the income of P1? options: A)s.800 B)s.2400 C)s.4000 D)s.3500 E)s.4200 SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their expenditures be Rs.3y and 2y respectively. Then, 5x – 3y = 1400 …(i) and 4x – 2y = 1400 ……..(ii) On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1400 -> x = 700 P1’s income = Rs 5*700 = Rs.3500 ANSWER:D #### D QUESTION:A basket contains 3 blue, 3 red and 3 yellow marbles. If 3 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted? options: A)2/21 B)3/25 C)1/6 D)9/28 E)11/24 SOLUTION:Probability of getting each color marble = (3C1*3C1*3C1)/9C3 = (3*3*3)/84 = 27/84 = 9/28 So answer is D #### D QUESTION:For 1rs 4p interest wat will be for 5000rs? options: A)350Rs B)450Rs C)200Rs D)30Rs E)448Rs SOLUTION:For 1rs , 4p interest for 5000rs, x x= 5000/1 * 4p ==> 20000 paise To express in rs, 20000/100 = 200rs ANSWER:C #### C QUESTION:In what ratio water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per litre? options: A)2:7 B)1:2 C)2:9 D)2:2 E)2:6 SOLUTION:Answer with Explanation: By the rule of allegation, i. C.P of 1 liter of water = 0 ii. C.P of 1 liter of milk = 12 iii. Mean price (p) = 8 iv. d – m = 12-8 = 4 v. m – c = 8-0 = 8  Ratio of water and milk = 4 : 8 = 1 : 2 Answer:B #### B QUESTION:34. The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 6 feet, and the diagonal of the rectangular plate was 10 ft. What is height of the of the cylinder? options: A)7 B)10 C)8 D)12 E)15 SOLUTION:Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, one side and thehypothenuse use pythagoreans theorem or properties of 3-4-5 triangles to solve for the other side, 8. Correct answer C. #### C QUESTION:The average age of students in section A of 125 students is 23 years and the average age of students in section B of 162 students is 25 years. Find the average age of students in both sections taken together? options: A)26 years B)30years C)15years D)24years E)20years SOLUTION:The required average = (125*23+162*25)/125+162 = 24 years Answer is D #### D QUESTION:In a survey of parents, exactly 7/8 of the mothers and 3/4 of the fathers held full-time jobs. If 60 percent of the parents surveyed were women, what percent of the parents did not hold full-time jobs? options: A)25.5% B)21.5% C)17.5% D)13.5% E)9.5% SOLUTION:Fathers without full-time jobs are 1/4*2/5 = 2/20 of all the parents surveyed. Mothers without full-time jobs are 1/8*3/5 = 3/40 of all the parents surveyed. The percent of parents without full-time jobs is 2/20 + 3/40 = 7/40 = 17.5% The answer is C. #### C QUESTION:A person was going through train from Bombay to Pune. After every five minutes he finds a train coming from opposite direction. Velocity of trains are equal of either direction. If the person reached Pune in one hour then how many trains he saw in the journey ? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:11 ANSWER:C #### C QUESTION:10 books are placed at random in a shelf. The probability that a pair of books will always be together is - options: A)1/5 B)1/3 C)1/4 D)118/2 E)21/4 SOLUTION:10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2! Required probability = 1/5 Answer: C #### C QUESTION:Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 45 miles per hour. How many miles from the station was train A overtaken by train B? options: A)100 B)120 C)140 D)160 E)180 SOLUTION:After two hours, Train A is ahead by 60 miles. Train B can catch up at a rate of 15 miles per hour. The time to catch up is 60/15 = 4 hours. In 4 hours, train A travels another 30*4 = 120 miles for a total of 180 miles. The answer is E. #### E QUESTION:The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 80 and n is not prime, what is the greatest possible value of f(n)? options: A)75 B)69 C)60 D)55 E)63 SOLUTION:Since we need the largest value of f (n), we will start with the largest option. Option A: 75 = 3*5*5. This is not a product of distinct prime numbers. Hence incorrect Option B: 69 = 3*23. This is a product of distinct prime numbers. Rest all the options are smaller that 69. Correct Option: B #### B QUESTION:In a forest 150 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest? options: A)150 B)750 C)1,250 D)1,500 E)2,500 SOLUTION:Given 150 deers were caught and they are tagged in the first slot. In the second slot , 50 were caught and 5 we tagged then 10% of them are tagged. Given this 10% approximates the percentage of tagged deer in the forest..here number is 150.. then 100% is 1500.. is the number of deers population in the forest.. Answer: D is correct answer.. #### D QUESTION:Which of the following numbers is divisible by 4? options: A)27767 B)10224 C)26778 D)26679 E)26711 SOLUTION:10224. This is the only option with last two digits divisible by 4 Answer:B #### B QUESTION:If each digit in the set of A = {1,2,3,4,5,6,7,8} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent? options: A)8! / 7! B)8! - 7! C)6*7! D)8!/2! E)7! SOLUTION:The answer should be the (total arrangements) - (arrangements when 2 and 5 are adjacent). The number of ways to arrange 8 units is 8! If we think of 2 and 5 as one single unit, the number of arrangements is 7! Note that 2 and 5 can have two arrangements, so we multiply by 2 to get 2*7! The total number of valid arrangements is 8! - 2*7! = 8*7! - 2*7! = 6*7! The answer is C. #### C QUESTION:A bullock-cart travels 24 kilometers in 3 hours and an another bullock-cart travels 120 kilometers in 2 hours. What will be the ratio of their speeds? options: A)2 : 15 B)1 : 5 C)2 : 3 D)3 : 2 E)None of these SOLUTION:First cart speed will be 24/3=8 Second cart speed is 120/2=60 So, ratio is 8/60=2/15 ANSWER:A #### A QUESTION:A certain bacteria colony doubles in size every day for 25 days, at which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit? options: A)6.33 B)7.5 C)10 D)15 E)24 SOLUTION:If there is one bacteria colony, then it will reach the limit of its habitat in 25 days. If there are two bacteria colonies, then in order to reach the limit of habitat they would need to double one time less than in case with one colony. Thus colonies need to double 24 times. Answer: E. Similar questions to practice: Hope it helps. #### E QUESTION:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $400 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds? options: A)3000 B)5000 C)2000 D)4000 E)6000 SOLUTION:So, we know that Shawn received 20% of the amount he invested in a year. We also know that in one year Shawn received $200, thus 0.2x = $200 --> x = $1,000. Since, he invested equal sums in his 2 bonds, then his total savings before investing was 2*$1,000 = $2,000. Answer:C #### C QUESTION:UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought less of Toyota than Honda at the ratio of 7:3. If 70% of the Toyota bought and 30% of the Honda bought were SUV’s. How many SUV’s did UBA capital buy in the aforementioned purchase? options: A)76% B)58% C)68% D)89% E)49% SOLUTION:let total no of Vehicles bought be 100, Toyota 70 and Honda 30, so total number of SUV's bought for Toyota and Honda respectively 70* 70/100=49 and 30* 30/100=9 so total 58 SUV's were bought out of 100 Vehicles bought..so required % is 58% ANSWER:B #### B QUESTION:The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 8 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week? options: A)30 B)20 C)11 D)14 E)6 SOLUTION:Given: mean=21 and SD=8 The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean ismean-1*SD=13 and 2 SD below the mean ismean-2*SD=5, so the number of hours that Pat watched television was between 5 and 13 hours. Answer: C #### C QUESTION:The value of (34.5*0.473*1.567)/(0.0673*23.25*7.57) is close to options: A)2 B)1.15 C)2.05 D)2.16 E)2.35 SOLUTION:(34.5*0.473*1.567)/(0.0673*23.25*7.57) = 25.5710895/11.845 = 2.16 ANSWER:D #### D QUESTION:The perimeter of a rhombus are 24 cm and 10 cm, the area and the perimeter of the rhombus is options: A)64 sq.m B)70 sq.m C)78 sq.m D)84 sq.m E)None SOLUTION:Solution Perimeter of the rhombus = 56 m Each side of the rhombus = 56 / 4 m = 14 m. Height of the rhombus = 5 m Area = (14 x 5) m² = 70 m² Answer B #### B QUESTION:In a consumer survey, 66% of those surveyed liked at least one of three products: 1, 2, and 3. 35% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 8% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:35 + 30 + 20 = 85 This number includes some people counted twice and some people counted three times. 85 - 66 = 19, and this number represents people counted twice or three times. 8% of the people are counted two extra times. The percentage of people counted one extra time is 19 - 8(2) = 3. The percentage of people who liked more than one product is 8% + 3% = 11%. The answer is C. #### C QUESTION:Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $30.60. What was the percentage profit? options: A)1% B)2% C)3% D)4% E)5% SOLUTION:A dozen toys cost $360, so each toy cost $30. selling price / cost price = 30.60 / 30 = 1.02 The percentage profit is 2%. The answer is B. #### B QUESTION:The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is options: A)277 B)668 C)119 D)177 E)121 SOLUTION:Number of words which can be formed = 5! - 1 = 120 - 1 = 119. Answer: C #### C QUESTION:The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? options: A)16 2/3% loss B)100/3% loss C)50/3% profit D)100/3% loss E)200/3% loss SOLUTION:Explanation: 15 CP = 18 SP 18 --- 3 CP loss 100 --- ? => 16 2/3% loss ANSWER IS A #### A QUESTION:Solve the given two equations and find the inequality of X and Y. (a) 3X^2+8X+4 = 0 and (b) 4Y^2-19Y+12= 0 options: A)If x>y B)If x>=y C)If x<y D)If x<=y E)x=y or relationship cannot be established SOLUTION:Solution:- Solving we get X= -2/3 or -2 Y= 3/4 or 4 C) #### C QUESTION:If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by options: A)330 B)340 C)350 D)360 E)370 SOLUTION:1 11 21 .......91 2 12 22........92 3 13 23........93 . . . .. . .. . . . . .. .. . .. . . . .. . . .. . ... there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column and diff of 6 and 9 is 3 so 3*1*10+3*10*10 = 330 ANSWER:A #### A QUESTION:If five chimpanzee can eat five mangoes in five minutes. How many minutes would it take for four chimpanzee to eat four mangoes ? options: A)5 minutes B)10 minutes C)8 minutes D)14 minutes E)20 minutes SOLUTION:A 5 minutes #### A QUESTION:The password for a computer account has to consist of exactly eight characters. Characters can be chosen from any of the following: letter of the alphabet, numerical digits from 0 to 9, a hyphen, or the exclamation mark. Upper-case letters (e.g., A) are considered different from lower-case letters (e.g., a), and characters can be repeated. Given these rules, how many different passwords are possible? options: A)2^9 B)2^14 C)2^18 D)2^40 E)2^48 SOLUTION:26 letters in the alphabet, 26*2 = 52 letters, since the password is case-sensitive. Accounting for possibilities of the other special characters we have; 26+26+10+1+1 = 64, or 2^6 possibilities per character of the password. Total number of possible combinations: (2^6)^8 = 2^48 ANSWER:E #### E QUESTION:The function g(p) is defined for integers p such that if p is even, g(p) = p/2 and if p is odd, g(p) = p + 5. Given that g(g(g(g(g(p))))) = 19, how many possible values for p would satisfy this equation? options: A)1 B)5 C)7 D)8 E)11 SOLUTION:Let me define terms: in g(p) = R p is argument, R is result, g() is function, in g(g(g(g(g(p))))), g1 is inner most, g5 is outermost for identification. From definition of function g, we can deduce that: If Result is even then two possibilities for argument = 1 Even 1 Odd If Result is odd then one possibility for argument = 1 Even Since final result = 19 = Odd Possibilities: g1:1 Even g2: 1*(Even,Odd ) =1 Even 1 Odd g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8 Ans D it is! #### D QUESTION:Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 20 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled? options: A)2 hours B)4 hours C)1 hour 30 min D)5 hours E)6 hours SOLUTION:in three minute 1/20+1/30-1/20=2/60 = 1/30 part is filled 3 min--------1/30 parts x min--------- 1 part(full) x=90 min =1 hour 30 min ANSWER:C #### C QUESTION:The price of a T.V. set worth Rs. 15000 is to be paid in 20 installments of Rs. 1500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be? options: A)29997 B)28088 C)13500 D)19000 E)2799 SOLUTION:Money paid in cash = Rs. 1500 Balance payment = (15000- 1500) = Rs. 13500 .Answer:C #### C QUESTION:The profits of QRS company rose 20% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? options: A)15% B)32% C)44% D)62% E)80% SOLUTION:Assume 100 in march , then 120 in April as 20% increase , Then 96 in may as 20% decrease from April , and then 144 in june which is 150% of 96 . So overall increase is from 100 to 144 is 44% Answer C #### C QUESTION:What approximate value should come in place of the question mark (?). 36.0001 ÷ 5.9998 × √? = 108.0005 options: A)325 B)316 C)256 D)16 E)18 SOLUTION:Using approximation, we get 36⁄6 × √? = 108 or, √? = 108⁄6 or, √? = 18 or, ? = 324 ≈ 325 Answer E #### E QUESTION:During a behavioral experiment in a psychology class, each student is asked to compute his or her lucky number by raising 7 to the power of the student's favorite day of the week (numbered 1 through 7 for Monday through Sunday respectively), multiplying the result by 3, and adding this to the doubled age of the student in years, rounded to the nearest year. If a class consists of 28 students, what is the probability that the median lucky number in the class will be a non-integer? options: A)0% B)10% C)20% D)30% E)40% SOLUTION:Student's age is integral value. In question, we are multiplying student's age by 2 and adding some 3* 7^x something over there. It means Even (2* age of students) + Odd (3) * 7 ^x (where x is day of week). We know that 7^x is always odd. (e.g. 7, 49, 243, 1701, and repeat). => 3* odd is again odd. 2 * age of students is always even. So final equation is even +odd = odd. Avg of any number of odd digits or any number of even digits can never be non integral value. So 0% is the answer A. #### A QUESTION:what no should be subtracted from 92555 to make it a perfect square ? options: A)128 B)158 C)178 D)139 E)140 SOLUTION:root 92555= 304.228 and 304^2=92416 92555-92416=139 should be subtracted from 92555 to make it a perfect square ANSWER:D #### D QUESTION:In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.] options: A) 0.33 B) 0.44 C) 33 D) 44 E) 55 SOLUTION:A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents; A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene. How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/12*33 = 33 cents. Answer: C. #### C QUESTION:A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 81 km downstream options: A)5 hours B)4 hours C)3 hours D)2 hours E)None of these SOLUTION:Explanation : Speed of the boat in still water = 22 km/hr speed of the stream = 5 km/hr Speed downstream = (22+5) = 27 km/hr Distance travelled downstream = 81 km Time taken = distance/speed = 81/27 = 3 hours. Answer : Option C #### C QUESTION:The area of the maximum size of the circle described from the 10 inch square? options: A)75.5 sq inch B)76.5 sq inch C)77.5 sq inch D)78.5 sq inch E)79.5 sq inch SOLUTION:10 inch square means sides of sq are 10inch then circle is within square so diameter would be 10 inch maximum and radius is 5inch so area of the circle is = pi*r*r=3.14*5*5=78.5 sq inch ANSWER:D #### D QUESTION:A train runs at the speed of 72 kmph and crosses a 250 metre long platform in 26 seconds. What is the length of the train ? options: A)220 metre B)230 metre C)250 metre D)260 metre E)270 metre SOLUTION:Distance covered in 26 seconds = 26×72×5/18=520 meter Length of the train = 520-250=270 meter ANSWER: E #### E <<<Examples ends QUESTION:The successive discounts 20% and 15% are equal to a single discount of? options: A)43% B)72% C)32% D)44% E)29% SOLUTION:C 32% Let the CP of an article be Rs. 100 Given that successive discounts are 20% and 15%. SP = 85% of 80% of 100 = (85/100)(80/100)(100) => SP = Rs. 68 Clearly, single discount is 32%. #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:At what rate of interest is an amount doubled in two years, when compounded annually? options: A)41.4% B)43.4% C)31.4% D)30% E)21.4% SOLUTION:Let the rate of interest be r. The amount gets doubled in two years => P(1 + r/100)2 = 2p => 1 + r/100 = √2 => r/100 = √2 - 1 = 0.414 => r = 100(0.414) = 41.4% ANSWER:A #### A QUESTION:Sonika deposited Rs.6200 which amounted to Rs.7200 after 5 years at simple interest. Had the interest been 3% more. She would get how much? options: A)9680 B)8130 C)8134 D)8556 E)9808 SOLUTION:(6200*5*3)/100 = 930 7200 -------- 8130 Answer: B #### B QUESTION:What is the largest integer n such that 2^n is a factor of 20^8 ? options: A)1 B)2 C)4 D)8 E)16 SOLUTION:20^8=(2^2∗5)^8=2^16 5^8 Therefore the largest integer n such that 2^n is a factor of 2^165^8 is 16. Answer: E. #### E QUESTION:What is the units digit of 3333^(333)*3333^(222)? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:Each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits. Here's another way to organize the information. We're given [(2222)^333][(3333)^222] We can 'combine' some of the pieces and rewrite this product as.... ([(2222)(3333)]^222) [(2222)^111] (2222)(3333) = a big number that ends in a 6 Taking a number that ends in a 6 and raising it to a power creates a nice pattern: 6^1 = 6 6^2 = 36 6^3 = 216 Etc. Thus, we know that ([(2222)(3333)]^222) will be a gigantic number that ends in a 6. 2^111 requires us to figure out thecycleof the units digit... 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 So, every 4powers, the pattern of the units digits repeats (2, 4, 8, 6.....2, 4, 8, 6....). 111 = 27 sets of 4 with a remainder of 3.... This means that 2^111 = a big number that ends in an 8 So we have to multiply a big number that ends in a 6 and a big number that ends in an 8. (6)(8) = 48, so the final product will be a gigantic number that ends in an 6. Final Answer: D #### D QUESTION:864.942 - ? + 45.76 = 547.905 options: A)A)899.015 B)B)752.804 C)C)714.642 D)D)362.797 E)of these SOLUTION:Explanation: 362.797 Answer: Option D #### D QUESTION:If the digits 35 in the decimal 0.00035 repeat indefinitely, what is the value of (10^5-10^3)(0.00035)? options: A)37 B)41 C)3.5e-05 D)35 E)3.5e-07 SOLUTION:99*0.35=34.65 approx. 35 Answer : B #### B QUESTION:On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price Q per glass on the second day? options: A) $015 B) $0.20 C) $0.30 D) $0.40 E) $0.45 SOLUTION:On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade; On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade; So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3. We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day. Say the price of the glass of the orangeade on the second day was $x then 2*0.6=3*x --> x=$0.4. Answer: D. #### D QUESTION:A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 300,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes? options: A)a) 500 B)b) 750 C)c) 1,000 D)d) 1,250 E)e) 1,500 SOLUTION:Since N = 2F, no of Florida zip codes (F) will be N/2. Since N = 4A, no of Arizona zip codes (A) will be N/4 Since N = (4/3)C, no of California zip codes (C) will be 3N/4 N + N/2 + N/4 + 3N/4 = 5N/2 = 250 N = 100 C = 3N/4 = 75 No of orders is 25% of 300,000 = 75,000 So required ratio = 75,000/75 = 1000 Answer C #### C QUESTION:6) A marketing firm determined that , of 180 households surveyed, 80 used neither Brand A nor Brand B soap.60 used only Brand A soap and for every household that used both brands of soap, 3 used only brand B soap.how many of the 200 household surveyed used both brands of soap? options: A)a) 15 B)b) 20 C)c) 30 D)d) 10 E)e) 45 SOLUTION:100 = At least one of Soap A or B Both brands = x Brand B = 3x => 60 + x + 3x = 100 => 4x = 40 => x = 10 Answer - D #### D QUESTION:If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true? i. s=0 ii. u is not equal to v iii.u > v options: A)None B)I only C)II only D)III only E)II and III SOLUTION:Notice two things: 1. we are asked to find out which of the following MUST be true, not COULD be true and 2. s, u, and v are positive integers. Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. . Answer: A #### A QUESTION:There are 3 teams each with 6 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice? options: A)50 B)23 C)108 D)28 E)45 SOLUTION:There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 36 possibilities (6*6) since each team has 6 players. So there are a total of 108 possibilities (36*3). I hope this method is easier for you to understand. #### C QUESTION:If x^2=3x+2, then x^3 = ? options: A)3x+2 B)6x+2 C)11x+6 D)8x-3 E)5x+4 SOLUTION:x^2 = 3x+2 x^3 = x*x^2 = x*(3x+2) = 3x^2 + 2x = 3(3x+2)+2x = 11x+6 The answer is C. #### C QUESTION:When 4 dice are thrown, what is the probability that the same number appears on each of them? options: A)1/36 B)1/18 C)1/216 D)1/5 E)1/4 SOLUTION:Sample space (Denominator): When 4 dice are thrown simultaneously, then the total number of possible outcomes is 64 = 1296. Event (Numerator): The chances that all the dice show same number (1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)} is 6. Probability = Event/ Sample space = 6/64 = 1/63 = 1/216. ANSWER:C #### C QUESTION:A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.300, find the original price per kg? options: A)s.7.7 B)s.7.4 C)s.7.5 D)s.7.1 E)s.7.9 SOLUTION:100*(20/100) = 20 --- 10 ? --- 1 => Rs.2 300 --- 80 ? --- 2 => Rs.7.5 Answer:C #### C QUESTION:If the length and breadth of a rectangular room are each increased by 1 m, then the area of floor is increased by 21 sq. m. If the length is creased by 1 m and breadth is decreased by 1m, then the area is decreased by 5 sq. m. The perimeter of the floor is: options: A)27 B)35 C)40 D)49 E)38 SOLUTION:Let length = x meters and breadth = y meters. Then, (x + 1) (y + 1) - xy = 21 x + y = 20 ………………1 And, xy - [(x + 1) (y - 1)] = 5 x - y = 6 ………………..2 Solving (i) and (ii), we get : x = 13 and y = 7 So, length = 13 m and breadth = 7 m. Perimeter = [2 (13 + 7)] m = 40 m. answer : C #### C QUESTION:A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 5,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? options: A) 1.25% B) 3.75% C) 6.25% D) 6.67% E) 11.11% SOLUTION:The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-5,500=4,500 gallons and sodium chloride is 500 gallons (5% of initial solution of 10,000 gallons) then sodium chloride is 500/4,500*100=~11.11% of the remaining solution of 4,500 gallons. Answer: E. #### E QUESTION:The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 2 and 4 slices per customer. How many slices cannot be bought? options: A)42. B)38. C)33. D)22. E)20. SOLUTION:Let X pizzas of 2 slices and Y pizzas of 4 slices. 2X + 4Y. Lets check options wise. A. 42 => 2(15) + 4(3) B. 38 => 2(15) + 4(2) C. 33 = we can't write anything with 5 and 8 series..Lets try 2(15) + 4(3) = 32 , 2(16) + 4(3) = 34 , nothing works out. D. 22 => 2(10) + 4(3) E. 20 => 2(6) + 4(2) Answer: correct option is C #### C QUESTION:The balance of a trader weighs 10% less than it should. Still the trader marks up his goods to get an overall profit of 20%. What is the mark up on the cost price? options: A)40% B)8% C)25% D)16.66% E)9% SOLUTION:Original cost before weight adjustment: X Cost after 90% weight adjustment: 9/10 X 20% profit on 9/10X: (120/100)(9/10)(X) or 108X/100 Mark up on original cost of X: (108X/100)/X-1 = 8/100 ANSWER:B #### B QUESTION:12 welders work at a constant rate they complete an order in 3 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order? options: A)5 B)2 C)8 D)4 E)6 SOLUTION:1. We need to find out the time taken by 3 workers after day 1. 2. total no.of wokers * total time taken = time taken by 1 worker 3. Time taken by 1 worker = 12*3 = 36 days 4. But on day 1 twelve workers had already worked finishing 1/3 of the job. So 3 workers have to finish only 2/3 of the job. 5. Total time taken by 3 workers can be got from formula used at (2). i.e., 3* total time taken = 36. Total time taken by 3 workers to finish the complete job is 36/ 3 = 12 days. 6. Time taken by 6 workers to finish 2/3 of the job is 2/3 * 12 =8 days. The answer is choice C #### C QUESTION:Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 12% vinegar, dressing P comprises what percentage of the new dressing? options: A)50% B)40% C)30% D)20% E)10% SOLUTION:Let x be the percentage of dressing P in the new dressing. 0.3x + 0.1(1-x) = 0.12 0.2x = 0.02 x = 0.1 = 10% The answer is E. #### E QUESTION:If a - b =6 and a2+b2=48 , find the value of ab. options: A)6 B)8 C)10 D)12 E)2 SOLUTION:Explanation: We know 2ab=(a2+b2)−(a−b)2 2ab=48−36=12 =>ab=6 Option E #### E QUESTION:A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? options: A)87 min B)82 min C)86 min D)47 min E)72 min SOLUTION:Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18 m = 120 m. Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min. Answer:D #### D QUESTION:If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is? . options: A)6 B)12 C)24 D)36 E)48 SOLUTION:72 x 1 = 72 72 x 2 = 144 14^4=12^2 Largest possible which can divide 12 is 12 Answer = B #### B QUESTION:A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? options: A)187 B)180 C)289 D)216 E)279 SOLUTION:Length of the train be ‘X’ X + 120/15 = X + 180/18 6X + 720 = 5X + 900 X = 180m Answer:B #### B QUESTION:In the quadratic equation ax2 - x - 12 = 0, if the sum of two roots is 1, what is the product of the two roots? options: A)-12 B)-6 C)12 D)6 E)24 SOLUTION:Explanation: The sum of the roots of the quadratic equation ax2 + bx + c = 0 are (-b/a) and the product of the roots are (c/a). Thus, in the equation ax2 - 11x + 40 = 0, where a = a, b = - 1 and c = -12. we get, sum of the roots = 1 / a = 1 a = 1 Product of the roots = -12 / 1 =-12 ANSWER: A #### A QUESTION:A six-sided die is rolled once. What is the probability that the number rolled is greater than 3? options: A)2 / 3 B)1 / 2 C)3 / 3 D)4 / 5 E)2 / 4 SOLUTION:Only 4, 5 & 6 so, 3 / 6 = 1/2 correct answer B #### B QUESTION:A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business? options: A)Rs. 7500 B)Rs. 9000 C)Rs. 9500 D)Rs. 10,000 E)None of these SOLUTION:Explanation: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3 B's share = 25000 * 3/10 = Rs. 7500. ANSWER IS A #### A QUESTION:A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? options: A)1350 B)2997 C)2087 D)2697 E)9824 SOLUTION:Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 2*2.5 => 675 675 * 2 = Rs.1350 Answer:A #### A QUESTION:A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.5 per sq m? options: A)6500 B)2779 C)2779 D)3900 E)2781 SOLUTION:Area = (l + b – d) d (80 + 60 – 10)10 => 1300 m2 1300 * 5 = Rs.6500 Answer:A #### A QUESTION:The volume of the sphere QQ is (dfrac{37}{64}%)less than the volume of sphere PP and the volume of sphere RR is (dfrac{19}{27}%) less than that of sphere QQ. By what is the surface areaof sphere RR less than the surfacearea of sphere PP? options: A)56% B)68% C)75% D)85% E)95% SOLUTION:Let the volume of sphere PP be 64 parts. Therefore volume of sphere QQ =64−3764%=64−3764% of 6464 =64−37=27=64−37=27 parts. The volume of RR =27−1927×27=27−1927×27 =27−19=8=27−19=8 parts. Volume ratio: =P:Q:R=64:27:8=P:Q:R=64:27:8 Radius ratio: =P:Q:R=4:3:2=P:Q:R=4:3:2 The surface area will be 16:9:516:9:5 Surface area of RR is less than the surface area of sphere PP 16k−4k=12k16k−4k=12k Now, =12k16k×100=12k16k×100 =75%=75% Thus surface area of sphere RR is less than the surface area of sphere P by 75% C #### C QUESTION:A store reduced the price of all items in the store by 12% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place? options: A)80.0 B)79.2 C)81.0 D)81.1 E)81.9 SOLUTION:consider price of the all items as $100 after a initial reduction of 12% price becomes = 0.88 *100 = $ 88 after the final reduction of 10% price becomes = 0.9* 88 = $ 79.2 price of all items on second day is 79.2% of price on first day correct answer option B #### B QUESTION:The sum of the first 50 positive even integers is 2,000. What is the sum of the odd integers from 101 to 200, inclusive? options: A) 5,050 B) 7,500 C) 8,050 D) 15,000 E) 19,600 SOLUTION:101+103+.......199 If we remove 100 from each of these it will be sum of 1st 100 odd numbers. so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050 Sum of 1st 50 positive even integers = 2000 sum of 1st 100 odd numbers = 5050 - 2000 = 3050 so 101+103+.......199 = 50 * 100 + (1+3+5+7+......) = 5000 + 3050 =8050 C is the answer. #### C QUESTION:It is required to seat 4 boys and 3 girls in a row so that the girls occupy the even places. How many such arrangements are possible? options: A)142 B)144 C)3680 D)3280 E)3680 SOLUTION:Total number of candidates = 4 + 3 = 7. In the row of 7 positions, the even places are 2nd, 4th, 6th . Now, number of even places = 3. Number of girls to occupy the even places = 3. Even places can be filled = P (3, 3) ways. Number of boys = 4. The remaining 4 places can be filled by 4 boys = P (4, 4) ways By the fundamental principle of counting: The required number of seating arrangements P(3, 3) x P(4, 4) = 3! x 4! = 6 x 24 = 144 ANSWER:B #### B QUESTION:A garrison of 1850 men has provisions for 28 days. At the end of 12 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement? options: A)1850 B)2960 C)3000 D)1110 E)1712 SOLUTION:1850 ---- 28 1850 ---- 16 x ----- 10 x*10 = 1850*16 x = 2960 1850 ------- 1110 Answer: D #### D QUESTION:Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 140 sandwiches were made, how many bologna sandwiches were made? options: A)15 B)30 C)38 D)42 E)49 SOLUTION:For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts and we should calculate how many sandwiches holds 1 part: 140 / 20 = 7 sandwiches in one part For bologna we have 7 parts so: 7 * 7 = 49 Answer is E #### E QUESTION:A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 8000. options: A)Rs. 2500 B)Rs. 8500 C)Rs. 7200 D)Rs. 8000 E)None of these SOLUTION:Explanation: A = 2B and B = 5C => A : B = 2 :1and B : C = 5 : 1 => A : B : C = 10 : 5 : 1 Ratio of capitals of A, B and C = 10 : 5 : 1 B's share = Rs.[(5/16) × 8000] = Rs. 2500 Answer: Option A #### A QUESTION:If the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is? options: A)A)15 B)B)10 C)C)14 D)D)12 E)E)11 SOLUTION:2 * 22/7 * 14 * x = 880 => x = 10 ANSWER:B #### B QUESTION:When positive integer A is divided by positive integer B, the result is 9.44. Which of the following could be the integer B is ? options: A)11 B)44 C)24 D)25 E)22 SOLUTION:the remainder will be obtained from the decimal part when A is divided by B i.e. 0.44 0.44 = 44/100 = 11/25 so possible remainders are 11,22,33,44. Only option A-11 satisfies this for remainder 11, A=236 and B=25 Ans - D #### D QUESTION:Klaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. Given these choices, how many candle + flower groupings can she select? options: A)54 B)72 C)96 D)144 E)432 SOLUTION:Klaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement.2 candles from 4 candles: 4C2: 6 8 flowers from 9 flowers: 9C8 : 9 So total grouping 9*6= 54. Answer is A. #### A QUESTION:Max scored 6 marks more than what he did in the previous examination in which he scored 30. Maria scored 30 marks more than she did in the previous examination in which she scored 60. Who showed less improvement? options: A)58% B)50% C)80% D)20% E)55% SOLUTION:Max percentage improvement in the first exam = (6/30 × 100) % = (600/30) % = 20 % Maria percentage improvement in the first exam = (30/60 × 100) % = (3000/60) % = 50 % Hence, 20 % < 50 % Therefore, Max showed less improvement. Answer:B #### B QUESTION:3 pig’s and 10 hens are brought for Rs.1200. If the average price of a hen be Rs.30. What is the average price of a pig. options: A)300 B)350 C)400 D)425 E)275 SOLUTION:Explanation: Average price of a hen = Rs.30 total price of 10 hens = 10*30 = Rs.300 But total price of 3 pigs and 10 hens = Rs. 1200 Total price of 3 pigs is = 1200 - 300 = 900 Average price of a pig = 900/3 = Rs. 300 Answer: A #### A QUESTION:Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: options: A)18 km/hr B)26 km/hr C)36 km/hr D)42 km/hr E)52 km/hr SOLUTION:Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/12 --> 2x = 20 --> x = 10. --> Speed of each train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr. Answer : C. #### C QUESTION:A school has received 30% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 60% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? options: A)$200 B)$250 C)$100 D)$350 E)$875 SOLUTION:Let us suppose there are 100 people. 60% of them donated $30000 ( 500 * 60 ) $30000 is 30% of total amount. So total amount = 30000 * 100/60 Remaining amount is 70% of total amount. 70% of total amount = 30000 * (100/60) * (70/100) = 35000 This amount has to be divided by 40 ( remaining people are 40 ) So per head amount is 35000/40 = $875; ANSWER:E #### E QUESTION:In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B? options: A)8 B)9 C)7 D)5 E)2 SOLUTION:Since A beats B by 200 m or 25 seconds, i t implies that B covers 200 m in 25 seconds. Hence speed of B = 200/25 = 8 m/s. Answer: A #### A QUESTION:If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference W between the greatest and least of the five integers? options: A)4K B)4k^2 -4k C)4-4k D)4 E)4k+4 SOLUTION:(n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1 => n = 10k - 5 Greatest = n + 2 = 10k - 5 + 2 = 10k - 3 Least = n - 2 = 10k - 5 - 2 => Difference W= 10k - 3 - (10k - 7) = 4 Answer - D #### D QUESTION:A train 480 m in length crosses a telegraph post in 16 seconds. The speed of the train is? options: A)22 kmph B)108 kmph C)54 kmph D)71 kmph E)88 kmph SOLUTION:S = 480/16 * 18/5 = 108 kmph Answer:B #### B QUESTION:A certain office supply store stocks 2 sizes of self-stick notepads, each in 8 colors. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible? options: A)6 B)8 C)16 D)124 E)128 SOLUTION:Notepads of the same color = 8 (we have 8 colors). As we have two sizes then total for the same color=8*2=16 Notepads of the different colors = 8C3=56 (we should choose 3 different colors out of 8). As we have two sizes then total for the different color=56*2=112 Total=112+16=128 Answer: E. #### E QUESTION:Divide Rs.116000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6.find the share of A? options: A)29491 B)28491 C)39491 D)49491 E)59491 SOLUTION:Compound ratio of A:B:C A:B = 3:4 B:C = 5:6 ---------- A:B:C = 15:20:24 We can divide Rs.116000 in this ratio. Share of A = 15/59 * 116000 = 29491 ANSWER:A #### A QUESTION:If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words? options: A)5 to 4 B)3 to 2 C)2 to 1 D)5 to 1 E)6 to 1 SOLUTION:Method #1: Using the permutation formula # of 5 letter code words: nPr = n! / (n – r)! = 10! / (10 – 5)! = 10*9*8*7*6 # of 4 letter code words: nPr = 10! / (10 – 4)! = 10*9*8*7 # of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8*7) = 6 = 6/1 Answer is E. #### E QUESTION:The cost price of 20 articles is equal to the selling price of 25 articles. The loss percent in the transaction is options: A)5 B)20 C)25 D)30 E)None of these SOLUTION:Let C.P. of 1 article = 1 then C.P. of 25 articles = 25 and S.P. of 25 articles = 20 ∴ loss % = 25−20/20×100=25% Answer C #### C QUESTION:3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day? options: A)34 B)77 C)36 D)49 E)38 SOLUTION:Explanation: Let the required length be x meters More men, More length built (Direct proportion) Less days, Less length built (Direct Proportion) \inline \fn_jvn \left.\begin{matrix} Men\: \: \: 20:35\\ Days\: 6:3 \end{matrix}\right\}::56:x \inline \fn_jvn \therefore (20 x 6 x X)=(35 x 3 x 56) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{35\times 3\times 56}{120} =49 Hence, the required length is 49 m. Answer: D #### D QUESTION:Y and Z start a business with Rs.3000 and Rs.6000 respectively. How should they share their profits at the end of one year? options: A)4:1 B)1:3 C)1:4 D)1:5 E)1:2 SOLUTION:They should share the profits in the ratio of their investments. The ratio of the investments made by Y and Z = 3000 : 6000 => 1:2 . Answer:E #### E QUESTION:The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the younger child insists of standing by his dog? options: A)12 B)24 C)30 D)48 E)120 SOLUTION:We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that C2 and D are always together. Consider F and M to be one unit, then we would have total of four units: {F}, {M}, {C1}, {C2D}. The number of arrangements of these four units is 4!, but C2 and D within their unit can be arranged in 2 ways: {C2D} or {DC2}, so total number of arrangements is 4!*2=48. Answer: D #### D QUESTION:If n is an integer and 5^n > 4,000,000, what is the least possible value of n? options: A)7 B)8 C)9 D)10 E)11 SOLUTION:When you separate the 4000000 into factors of 5 and 2 you get - > 10^6 x 2^2 = 5^6 x 2^8 2 to the ^ 8 = 256 so its 256 x 5^6 that means 5^6 x 5^x must be greater 5^x > 256 5^1=5 5^2=25 5^3= 125 5^4= 625 - > so x must be at least 4 5^(6+4)= 5^10 ANSWER:D #### D QUESTION:The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder? options: A)308 sq cm B)220 sq cm C)440 sq cm D)132 sq cm E)138 sq cm SOLUTION:r = 7 h = 3 2πr(h + r) = 2 * 22/7 * 7(10) = 440 ANSWER:C #### C QUESTION:A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? options: A)72 Kmph B)28 Kmph C)29 Kmph D)65 Kmph E)25 Kmph SOLUTION:Length = Speed * time Speed = L/T S = 400/20 S = 20 M/Sec Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer:A #### A QUESTION:If inflation increases at a rate of 8 p.c.p.a. what will a 20 article cost at the end of two years? options: A)Between 20 and 21 B)Between 21 and 22 C)Between 22 and 23 D)Between 23 and 24 E)None of these SOLUTION:Required sum = 20(1+8/100)2=20×27×27/25×25=23.3 Answer D #### D QUESTION:Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work? options: A)20 B)34 C)38 D)40 E)46 SOLUTION:We have that X/24 - (60-X)/2R = 40 Also X/R - (60-X)/2R = 120 So we get that 2x - 60 = 80R 3x - 60 = 240R Get rid of R 120 = 3x x = 40 Hence answer is D #### D QUESTION:Sangakara and Ponting select batting by using a dice, but dice is biased. So to resolve,Ponting takes out a coin. What is the probability that coin shows correct option? options: A)1/2 B)1/6 C)1/12 D)6/10 E)3/10 SOLUTION:as coin has only two faces then probability must be 1/2 ANSWER:A #### A QUESTION:Let x be a positive integer, what is the remainder when 4^(2x+5)+3 is divided by 5? options: A)2 B)3 C)4 D)1 E)5 SOLUTION:For: (4^(2x+5)+3)/5 Let n = 2x + 5 4^n 4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256, last digit pattern repeats 4, 6, 4, 6, .... Rule: x^(m+n) = (x^m)(x^n) (4^(2x))(4^5) Rule: x^(mn) = (x^m)^n (4^2)(4^x)(4^5) => Now, (6)(4)(4) + 3 = (6) + 3 => Finally, 9/5 and remainder is 4. Answer: C #### C QUESTION:A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup? options: A)7/11 B)6/7 C)1/5 D)2/7 E)None of these SOLUTION:Explanation : Let, the vessel initially contains 8 litres of liquid. Let x litres of this liquid be replaced with water then quantity of water in new mixture =>3−(3x/8)+x litres. Quantity of syrup in new mixture =5−5x/8 litres. Therefore, =>3−(3x/8)+x=5−5x/8. =>5x+24=40−5x. =>x=8/5. So part of the mixture replaced, =>(8/5)×(1/8)=1/5. Answer : C #### C QUESTION:It takes Kannan 10 minutes to walk to the car park and 110 min to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.? options: A)8:50 a.m B)5:50 a.m C)7:50 a.m D)6:50 a.m E)7:00 a.m SOLUTION:The time it takes Kannan to get to work: time to walk to car park + time to drive 10 + 110 = 120 minutes = 2 hours Kannan needs to get out of the house 2 hours before 9:00 am at 9:00 - 2:00 = 7:00 a.m correct answer E #### E QUESTION:If each of 3 digit code is formed of integers from 1 to 30, inclusively, and each of the digits are different, how many possible codes are there? options: A)22896 B)25423 C)26980 D)24698 E)24360 SOLUTION:Code consists of 3 digits and no digit is repeated. First digit of the code can have 30 possibilities Second digit can have 29 possibilities Third digit can have 28 possibilities Total number of possible codes = 30*29*28 = 24360 Answer: E #### E QUESTION:The average successfull Search time for sequential search on n items is options: A)n/2 B)(n-1)/2 C)(n+1)/2 D)log(n)+1 E)(n)+1 SOLUTION:To understand this think as there is an array and now you are searching for an element which is a[0] element in that arrary...so for this you need to do 1 comparison. Now similarly for sequential searching suppose your are looking for an element which is present at 2nd position i.e a[1] position of that array then you will get answer within 2 comparisons. Now similarly if you have n elements and your desired element is the nth element then you will have to do n comparisons. so we can write total search time will be: (1+2+3+........+n) average search time will be (1+2+3+........+n)/n NOW we know sum of n natural numbers i.e 1+2+3+.....n= {n(n+1)}/2 ANSWER: C #### C <<<Examples ends QUESTION:The speed at which a girl can row a boat in still water is 90 kmph. If she rows downstream, where the speed of current is 18 kmph, what time will he take to cover 330 metres? options: A)11 B)12 C)13 D)14 E)15 SOLUTION:Speed of the boat downstream = 90 + 18 = 108 kmph = 108 * 5/18 = 30 m/s Hence time taken to cover 330 m = 330/30 = 11 seconds. Answer: A #### A

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:Bruce purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? options: A)1040 B)1050 C)1055 D)1065 E)1075 SOLUTION:Cost of 8 kg grapes = 70 × 8 = 560. Cost of 9 kg of mangoes = 55 × 9 = 490. Total cost he has to pay = 560 + 490 = 1055 C #### C QUESTION:A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it? options: A)23 days B)16 days C)11 days D)24 days E)35 days SOLUTION:D 24 days 2c = ¼ + 1/6 – 1/3 = 1/12 c = 1/24 => 24 days #### D QUESTION:A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of B? options: A)2160 B)3000 C)3018 D)3019 E)3012 SOLUTION:60*5:36*6:75*3 100: 72: 75 72/247 * 7410 = 2160 Answer: A #### A QUESTION:In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, or 4 is obtained. Angel played the game, getting at least one score of each of 1, 2, 3, and 4, and never getting the same score in consecutive steps. What is the greatest possible score that Angel could have gotten? options: A)15 B)18 C)21 D)23 E)29 SOLUTION:There are two conditions: 1. Angel got at least one score of each of 1, 2, 3, and 4. 2. She never got the same score in consecutive steps. Taking that into account, the greatest possible score that Angel could have gotten is 4 + 1 + 4 + 2 + 4 + 3 = 18. Answer: B. #### B QUESTION:A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year? options: A)59020 B)59299 C)59020 D)59300 E)59008 SOLUTION:Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500. Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000. Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P) Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally. Income of A = Twice the income of B (2500 + 18000 + P) = 2(P) P = 20500 Total profit = 2P + 18000 = 2*20500 + 18000 = 59000 Answer: D #### D QUESTION:180 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children? options: A)1~10 B)10~20 C)35~45 D)65~75 E)85~95 SOLUTION:180 = 2^2*3^3*5 There are factors in each range except for 65~75 The answer is D. #### D QUESTION:Two goods trains each 375 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? options: A)40 B)45 C)48 D)51 E)36 SOLUTION:Relative speed = 45 + 30 = 75 km/hr. 75 * 5/18 = 125/6 m/sec. Distance covered = 375 + 375 = 750 m. Required time = 750 * 6/125 = 36 sec. Answer: Option E #### E QUESTION:In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 140 marks, the no of questions he attempts correctly is : options: A)35 B)38 C)40 D)42 E)44 SOLUTION:Explanation: Let the number of correct answers be X. Number of incorrect answers = (60 – X). 4x – (60 – x) = 140 => 5x = 200 => x = 40 Answer: C #### C QUESTION:35 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days? options: A)87 B)18 C)42 D)16 E)10 SOLUTION:Binders Books Days 35 1400 21 x 1600 20 x/35 = (1600/1400) * (21/20) => x = 42 Answer:C #### C QUESTION:A train runs at the speed of 72 kmph and crosses a 250 metre long platform in 26 seconds. What is the length of the train ? options: A)220 metre B)230 metre C)250 metre D)260 metre E)270 metre SOLUTION:Distance covered in 26 seconds = 26×72×5/18=520 meter Length of the train = 520-250=270 meter ANSWER: E #### E QUESTION:if a person cover 3/5 part of his journey by train,7/20 part of his journey by bus and rest 6.5 km. by walk.what is total distance of his journey? options: A)65 km B)100 km C)120 km D)130 km E)75 km SOLUTION:let total distance be=x km.then, 3x/5+7x/20+6.5=x;12x+7x+130=20x;x=130 hence total distance=130 km. answer D #### D QUESTION:An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 40% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount? options: A)91.23% B)95.56% C)97.86% D)101.45% E)103.68% SOLUTION:0.6*1.2^3 = 1.0368 The answer is E. #### E QUESTION:If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of r − s? options: A)8 B)2 C)− 2 D)− 3 E)− 5 SOLUTION:Given: x^2 − 2x − 15 = (x + r)( x + s) Factor to get: (x - 5)(x + 3) = (x + r)( x + s) Rewrite as: (x + -5)(x + 3) = (x + r)( x + s) So, it's possible that r = -5 and s = 3 Here, r - s = (-5) - 3 = -8 Try REVERSING the factorization: x^2 − 2x − 15 = (x + r)( x + s) Factor to get: (x + 3)(x - 5) = (x + r)( x + s) Rewrite as: (x + 3)(x + -5) = (x + r)( x + s) So, it's possible that r = 3 and s = -5 Here, r - s = 3 - (-5) = 8 Answer: A #### A QUESTION:A scooter costs 30,000 when it is brand new. At the end of each year, its value is only 80% of what it was at the beginning of the year. What is the value of the scooter at the end of 3 years? options: A)10,000 B)12,500 C)12,800 D)12,000 E)15,360 SOLUTION:After first year, the value of the scooter = 24,000 After second year, the value of scooter = 19,200 After third year, the value of scooter = 15,360 Answer E #### E QUESTION:A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 5 meters apart,then at what speed is the train traveling? options: A)100km/hr B)110km/hr C)50km/hr D)150km/hr E)200km/hr SOLUTION:Number of gaps between 51 telephone posts = 50 Distance traveled in 1 minute = 50*50 = 2500m = 2.5km Speed = 60*2.5=150km/hr Answer is D #### D QUESTION:A man invested an amount of Rs.8000 in a fixed deposit scheme for 2 years at compound interest of 5% per annum. How much amount will Albert get on maturity of the fixed deposit ? options: A)Rs.8600 B)Rs.8620 C)Rs.8820 D)Rs. 8840 E)Rs. 8940 SOLUTION:Amount = 8000 *1+(5/100)2 = 8000 *21/20 * 21/20 = Rs.8820 ANSWER:C #### C QUESTION:A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? options: A)3630 B)3637 C)3630 D)3631 E)3635 SOLUTION:6300:4200:10500 3:2:5 3/10 * 12100 = 3630 Answer: A #### A QUESTION:Krishna's monthly expenditure was decreased by 50% and subsequently increased by 50%. How much percent does he loss? options: A)25 % B)50 % C)75 % D)85 % E)None of these SOLUTION:Explanation : Let the original expenditure = Rs. 100. New final expenditure = 150% of (50% of Rs. 100) = Rs.(150/10050/100100) = Rs. 75. Decrease = 100- 75 = 25 % Answer : A #### A QUESTION:If (5+k)(5-k)=(5^2)-(2^3),then what is the value of K? options: A)1 B)3 C)4 D)2 E)6 SOLUTION:Obviously,It is in the formula a^2-b^2=(a+b)(a-b) So k is 2 Option D #### D QUESTION:2 chairs and 1 table cost $110. 4 chairs and 1 table cost $166. How much does one chair cost? options: A)26 B)56 C)110 D)28 E)54 SOLUTION:Let the cost of 1 chair = x, let the cost of 1 table = y 2x + y = 110 y = 110 - 2x Again, 4x + y = 166 4x + (110 - 2x) = 166 4x + 110 - 2x = 166 2x + 110 = 166 2x = 56 x = 28 Answer: D #### D QUESTION:Suppose f(x) is an odd function for which f(x + 2) = f(x) for all x, and f(x) = x2nd for xε2 (0,1). Compute f(-3/2) + f(1). options: A)-1 B)-1/2 C)-1/4 D)1/4 E)1/2 SOLUTION:Because f is periodic, we know that f(-3/2) = f(1/2) = (1/2)2 = 1/4. Because f is odd, we know that f(1) = -f(-1), but because f is periodic, f(1) = f(-1). Therefore, f(1) = 0 and the answer is 1/4. correct answer D #### D QUESTION:In an animal behavior experiment, 25 tagged white pigeons and 250 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory? options: A)80.5 B)82 C)81.5 D)85 E)81.25 SOLUTION:Weighted mix method is best here.... Ratio is 1:10 for 88:80.5... So the answer required = 80.5+ (88-80.5)*1/10=80.5+7.5*1/10 80.5+0.75=81.25 E #### E QUESTION:A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? options: A)210m B)240m C)963m D)874m E)578m SOLUTION:Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B)240m #### B QUESTION:A positive whole number has factors of 3 and 4. The number MUST be divisible by: I. 12 II. 24 III. 48 options: A)I B)I & III C)II D)II & III E)III SOLUTION:12 , 24 is not divisible by 48.But 48 is divisible by 3,4,12,24. So answer is III Answer : E #### E QUESTION:John had a stock of 700 books in his bookshop. He sold 50 on Monday, 82 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold? options: A)26.5% B)50% C)46.5% D)56.5% E)60% SOLUTION:Let N be the total number of books sold. Hence N = 50 + 82 + 64 + 78 + 135 = 280 Let M be the books NOT sold M = 700 - N = 700 - 280 = 420 Percentage Books not sold / total number of books = 420/700= 0.60 = 60% correct answer E #### E QUESTION:24 machines can do a work in 10days. How many machines are needed to complete the work in 40days? options: A)10 B)6 C)4 D)7 E)5 SOLUTION:Required number of machines = 24*10/40 = 6 Answer is B #### B QUESTION:A and B are two partially filled buckets of water. If 4 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 5 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water? options: A)47/5 B)13 C)17 D)21 E)23 SOLUTION:Let A contains A, B contains B liters so, (A-4)/(B+4)= 1/3.......(1) again, (B-5)/(A+5)= 1/2..........(2) from (1)(2) we find A= 47/5 ans: (A) #### A QUESTION:There are 4 copies of 5 different jeans. In how many ways can they be arranged on a shelf? options: A)20!/4! B)20!/5(4!) C)20!/(4!)^5 D)20! E)5! SOLUTION:There are 4 copies of 5 different jeans.20!/((4!)^5) Answer - C #### C QUESTION:A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make? options: A)30% B)75% C)40% D)70% E)None of these SOLUTION:The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150 Profit(%) = (31150 - 17800)/17800* 100 = 75% ANSWER:B #### B QUESTION:A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in? options: A)17 hr B)19 hr C)10 hr D)14 hr E)16 hr SOLUTION:Work done by the tank in 1 hour = (1/2 - 1/3) = 1/14 Leak will empty the tank in 14 hrs. Answer:D #### D QUESTION:I. m-14, m, m, m, m+14 II. b, b+1, b+2, b+3, b+4 III. c, c, c, c, c The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following? options: A)I, II, III B)I, III, II C)II, III, I D)III, I, II E)III, II, I SOLUTION:S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of m or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end. A. #### A QUESTION:How many different ways can you select a pilot and a co pilot if you have 30 people to choose from? options: A) 870 B) 920 C) 1398 D) 4950 E) 9900 SOLUTION:You are not just choosing two from 30. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot. So the answer is in a sense (30C2) x 2 = 870. Ans A #### A QUESTION:The tailor has a 10 meter long piece of fabric for which to sew a ball room dress. She has to cuts this fabric into strips of 200 centimeters each. How long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ? options: A)150 B)200 C)188 D)245 E)123 SOLUTION:The tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes. The answer is D #### D QUESTION:By selling 99 pens, a trader gains the cost of 11 pens. Find his gain percentage? options: A)11 1/3% B)11 7/3% C)11 1/8% D)11 1/3% E)11 1/9% SOLUTION:Let the CP of each pen be Rs. 1. CP of 99 pens = Rs. 99 Profit = Cost of 11 pens = Rs. 11 Profit% = 11/99 * 100 = 11 1/9% Answer: E #### E QUESTION:If y ≠ 3 and 2a/y is a prime integer greater than 2, which of the following must be true? I. xa= y II. y = 1 III. a and y are prime integers. options: A) None B) I only C) II only D) III only E) I and II SOLUTION:Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer. So we should try to make the listed statements not true for some x and y (which satisfy y≠3 and 2x/y=prime>2). I. a = y --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2); II. y=1 --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2); III. a and y are prime integers --> not necessarily true: a=10 and y=4 (2a/y=5=prime>2). Answer: A. #### A QUESTION:If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 36 more than n. What is y in terms of x ? options: A)x-2 B)x-4 C)x+4 D)x-3 E)x-1 SOLUTION:Original Digits=xy i.e. Number=10x+y After reversing the digits: Digits=yx i.e. Number=10y+x 10y+x is 36 more than 10x+y 10x+y+36=10y+x 10x-x+36=10y-y 9x+36=9y x+4=y OR y=x+4 Answer : C #### C QUESTION:650 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ? options: A)a) 162 B)b) 138 C)c) 60 D)d) 38 E)e) 13 SOLUTION:Passed in english = 65% Passed in maths = 55% Passed in both = 40% of 55% = 2/5 * (55%) = 22% Passed in (English + Maths - Both + Neither) = 100% 65 + 55 - 22 + Neither = 100 Neither = 100 - 98 = 2% = 0.02 * 650 = 13 Answer: E #### E QUESTION:The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.2 the sixth number is? options: A)10.3 B)11.3 C)11.8 D)11.5 E)11.1 SOLUTION:1 to 11 = 11 * 10.9 = 119.9 1 to 6 = 6 * 10.5 = 63 6 to 11 = 6 * 11.2 = 67.2 63 + 67.2 = 130.2 – 119.9 = 10.3 6th number = 10.3 Answer: A #### A QUESTION:The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 168,000. What was the percent increase in the cost of the home? options: A)60% B)50% C)55% D)40% E)33.3% SOLUTION:Increase = 168000-120000 = 48000 % increase = 48000*100/120000 = 40% Answer: option D #### D QUESTION:How many seconds will a 900 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? options: A)22 B)54 C)99 D)77 E)12 SOLUTION:Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 900 * 3/50 = 54 sec. Answer: B #### B QUESTION:Out of 470 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ? options: A)80 B)150 C)100 D)180 E)220 SOLUTION:n(A)=325,n(B)=175,n(AuB)=470-50=420. Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-420=80. Answer is A #### A QUESTION:A and B start a business with Rs.6000 and Rs.18000 respectively. Hoe should they share their profits at the end of one year? options: A)3:5 B)3:4 C)3:1 D)1:3 E)3:9 SOLUTION:They should share the profits in the ratio of their investments. The ratio of the investments made by A and B = 6000 : 18000 => 1:3 Answer:D #### D QUESTION:All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A? options: A)1200 B)1723 C)1129 D)2613 E)1372 SOLUTION:A B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k. Quantity of milk in B = 8k - 5k = 3k. Quantity of milk in container C = 8k - 3k = 5k Container: A B C Quantity of milk: 8k 3k 5k It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk. 5k - 150= 3k + 150 => 2k = 300 => k = 150 The initial quantity of milk in A = 8k = 8 * 150= 1200 liters. #### A QUESTION:Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 249 marks in the second test and failed by 66 marks in that test. Find the pass mark in the first test? options: A)768 B)243 C)246 D)280 E)224 SOLUTION:Let the maximum mark in each test be M. The candidate failed by 66 marks in the second test. pass mark in the second test = 249 + 66 = 315 45/100 M = 315 Pass mark in the first test = 40/100 M = 40/45 * 315 = 280. Answer:D #### D QUESTION:How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 42 kmph? options: A)21.4 sec B)77 sec C)25 sec D)18 sec E)17 sec SOLUTION:D = 100 + 150 = 250 S = 42 * 5/18 = 11.7 mps T = 250/11.7 = 21.4 sec Answer:A #### A QUESTION:Rahul went to a shop and bought things worth Rs. 25, out of which 36 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? options: A)19 B)18.7 C)19.9 D)21.7 E)22.8 SOLUTION:Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 36 Paise is given as tax => Total tax incurred = 36 Paise = Rs.36/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−36/100−x)6/100 = 36/100 ⇒ 6(25 −0.36 −x) = 36 ⇒ (25 − 0.36 − x) = 6 ⇒ x = 25 − 0.36 − 6 = 18.7 B) #### B QUESTION:Pipe A can fill a tank in 6 hours, pipe B in 4 hours, and pipe C in 12 hours. If all the pipes are open, in how many hours will the tank be filled? options: A)1.5 B)2 C)2.5 D)3 E)3.5 SOLUTION:The part filled by A + B + C in 1 hour = 1/6 + 1/4 + 1/12 = 12/24 = 1/2 All the three pipes together will fill the tank in 2 hours. The answer is B. #### B QUESTION:The product of n^2 consecutive positive integers is always divisible by options: A)n^2 -1 B)(n+1)! C)2n +1 D)n^2 + 1 E)n! SOLUTION:Plug in some vlues and check - Product of first 2 number is 2*1 Product of first 3 number is 3*2*1 Product of first 4 number is 4*3*2*1 Product of first 5 number is 5*4*3*2*1 So, The product of first n natural numbers is always divisible by n! , answer will be (A) #### A QUESTION:JOHN and ANDREW can finish the work 9 days if they work together. They worked together for 6 days and then ANDREW left. JOHN finished the remaining work in another 6 days. In how many days JOHN alone can finish the work? options: A)30 days B)60 days C)18 days D)80 days E)90 days SOLUTION:Amount of work done by JOHN and ANDREW in 1 day = 1/9 Amount of work done by JOHN and ANDREW in 6 days = 6 × (1/9) = 2/3 Remaining work – 1 – 2/3 = 1/3 JOHN completes 1/3 work in 6 days Amount of work JOHN can do in 1 day = (1/3)/6 = 1/18 => JOHN can complete the work in 18 days Answer : C #### C QUESTION:If |4x+6| = 50, what is the sum of all the possible values of x? options: A)2 B)-2 C)4 D)-3 E)6 SOLUTION:There will be two cases 4x+6= 50 or 4x+6 = -50 => x =11 or x= -14 sum of both the values will be -14 +11 = -3 Answer is D #### D QUESTION:The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.2200, then what is the income of P1? options: A)s.800 B)s.2400 C)s.4000 D)s.5500 E)s.4200 SOLUTION:Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their expenditures be Rs.3y and 2y respectively. Then, 5x – 3y = 2200 …(i) and 4x – 2y = 2200 ……..(ii) On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 2200 -> x = 1100 P1’s income = Rs 5*1100 = Rs.5500 ANSWER:D #### D QUESTION:Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ? options: A)2:3:9 B)24:25:36 C)7:6:10 D)12 : 15 : 16 E)None of these SOLUTION:Explanation: Aman : Rakhi : Sagar =(70000×36)=(70000×36) :(105000×30):(105000×30) :(140000×24):(140000×24) =12:15:16=12:15:16. ANSWER IS D #### D QUESTION:A certain company reported that the revenue on sales increased 50 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? options: A)50 % B)40 % C)35 % D)32 % E)20 % SOLUTION:Assume the revenue in 2000 to be 100. Then in 2003 it would be 150 and and in 2005 180, so from 2003 to 2005 it increased by (180-150)/150=30/150=20%. Answer: E. #### E QUESTION:There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 4:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ? options: A)9:6 B)3:2 C)118:126 D)193:122 E)201:132 SOLUTION:m=portion of milk in solution m=(4/7+2/3+3/5)/3➡193/315 315-193=122 122/315=portion of water in solution ratio of milk to water=193/122 ANSWER:D #### D QUESTION:In a Private Company 20 Nos. staffs are employed. In a Festival season their Boss give festival allowance to all. He says his accountant to calculate for 30 days @ 100. Also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash. He had given Rs.65000/- to the accountant. How much amount will taken from Petty cash? options: A)A)1000 B)B)3000 C)C)3500 D)D)2500 E)E)2250 SOLUTION:For 20 staffs: 300*100*20 = 60000 for driver and cleaning staff: 300*100*2 =6000 From petty Cash : 1000 Answer is 1000 Answer is A #### A QUESTION:A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)3% B)4% C)5% D)6% E)7% SOLUTION:S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate =(100 x 3000)/(12500 x 4)% = 6% answer :D #### D QUESTION:A car covers a distance of 829 km in 7 hours. Find its speed? options: A)104 kmph B)289 kmph C)118 kmph D)277 kmph E)177 kmph SOLUTION:829/7 = 118 kmph Answer: C #### C QUESTION:The true discount on a bill of Rs.1080 is Rs.180.The banker's discount is options: A)210 B)212 C)214 D)216 E)None of these SOLUTION:Solution P.W = Rs.(1080 - 180) = Rs. 900 S.I on Rs. 1080 =Rs.(180/900 x 1080) = Rs. 216. Answer D #### D QUESTION:A sum of money deposited at C.I. amounts to Rs.3000 in 3 years and to Rs.3600 in 4 years. Find the rate percent? options: A)25% B)5% C)10% D)15% E)20% SOLUTION:3000 --- 600 100 --- ? => 20% Answer: E #### E QUESTION:In a simultaneous throw of 2 dice what is the probability of getting a total of 4? options: A)1/2 B)1/4 C)2/9 D)1/12 E)3/13 SOLUTION:n(S) = 6*6 = 36 E = {(1,3),(2,2),(3,1)} Probability = 3/36 = 1/12 Answer is D #### D QUESTION:Thompson had the following scores in an exam (out of 100): Social Studies: 60 Science: 89 Art: 62 Music: 69 Spanish:84 Biology: 89 What are his average marks ? options: A)61.5 B)72.5 C)71.5 D)85.5 E)75.5 SOLUTION:Explanation: Average = (60 + 89 + 62 + 69 + 84 + 89)/ 6 = 375/5 = 75. Answer: E) 75.5 #### E QUESTION:Jill, who lives in City C, plans to visit 3 different cities, M, L, and S. She plans to visit each city exactly once and return to City C after the 3 visits. She can visit the cities in any order. In how many different orders can she visit the 3 cities? options: A)3 B)6 C)8 D)9 E)12 SOLUTION:3! = 6 M L S C M S L C L M S C L S M C S M L C S L M C She can visit the cities in any order. Number of ways of arranging the three cities is 3! = 6 ways. Hence B. #### B QUESTION:What is the units digit of 3333^(333)*3333^(222)? options: A)0 B)2 C)4 D)6 E)8 SOLUTION:Each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits. Here's another way to organize the information. We're given [(2222)^333][(3333)^222] We can 'combine' some of the pieces and rewrite this product as.... ([(2222)(3333)]^222) [(2222)^111] (2222)(3333) = a big number that ends in a 6 Taking a number that ends in a 6 and raising it to a power creates a nice pattern: 6^1 = 6 6^2 = 36 6^3 = 216 Etc. Thus, we know that ([(2222)(3333)]^222) will be a gigantic number that ends in a 6. 2^111 requires us to figure out thecycleof the units digit... 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 So, every 4powers, the pattern of the units digits repeats (2, 4, 8, 6.....2, 4, 8, 6....). 111 = 27 sets of 4 with a remainder of 3.... This means that 2^111 = a big number that ends in an 8 So we have to multiply a big number that ends in a 6 and a big number that ends in an 8. (6)(8) = 48, so the final product will be a gigantic number that ends in an 6. Final Answer: D #### D QUESTION:A construction company wants to number new houses using digit plates only. If the company puts an order for 912 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1). options: A)320 B)350 C)340 D)360 E)400 SOLUTION:You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there? 99+(912-9-90*2)/3=340 Answer : C #### C <<<Examples ends QUESTION:A, Band C are three contestants in a kmrace. If A can give B a start of 40 m and A can give C a start of 64m how many metre's start can B give C ?. options: A)540 m B)178 m C)936 m D)234 m E)713 m SOLUTION:While A covers 1000 m, B covers (1000 - 40) m = 960 m and C covers (1000 - 64) m or 936 m. When B covers 960 m, C covers 936 m Option C #### C

Given a mathematics or algebraic problem, Think step by step , then print '####' and finally give your final answer. Examples starts>>> QUESTION:A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases? options: A)500bc B)500b/c C)1000bc D)1000b/c E)1000/bc SOLUTION:2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips The answer is C. #### C QUESTION:A father was as old as his son's present at the time of your birth. If the father's age is 44 years now, the son's age 5years back was? options: A)10 years B)12 years C)14 years D)16 years E)17 years SOLUTION:Let the son's present age be x years. Then, (44 - x) = x 2x = 44. x = 22. Son's age 5 years back (22 - 5) = 17 years. E #### E QUESTION:Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is? options: A)81.6 B)88.6 C)81.1 D)81.5 E)81.2 SOLUTION:SI = 40 + 40 CI = 40 + 40 + 1.6 = 81.6 Answer: A #### A QUESTION:If e<0, which of the following must be true? options: A)–100 < e < 100 B)e ≤ –1 C)e ≤ 1 D)e^2 ≥ 1/4 E)–100 < e < 0 SOLUTION:e is a negative number. A. –100 < e < 100e can be a negative number less than -100 B. e ≤ –1e can be a fraction, in which case it would be greater than -1 C. e ≤ 1must be true since 1 is positive and e is negative D. e^2 ≥ 1/4not true if e is a negative fraction like -1/5 E. –100 < e < 0e can be a negative number less than -100=C #### C QUESTION:A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 37 years and that of the grandchildren is 6 years. What is the average age of the family? options: A)28 4⁄7 years B)31 5⁄7 years C)32 2⁄7 years D)27 1⁄2 years E)None of these SOLUTION:Required average = (67×2+37×2+6×3/2+2+3) =226/7 = 32 2⁄7 years Answer C #### C QUESTION:A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum? options: A)7000 B)7029 C)7290 D)7010 E)7102 SOLUTION:Let the sum be Rs. x. (x * 18 * 2)/100 - (x * 12 * 2)/100 = 840 => 36x/100 - 24x/100 =840 => 12x/100 = 840 => x = 7000. Answer:A #### A QUESTION:How many words with or without meaning, can be formed by using all the letters of the word, ‘POWER’, using each letter exactly once? options: A)700 B)720 C)750 D)800 E)120 SOLUTION:The word ‘POWER’ contains 5 different letters. Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time =5P5 = 5! = 5*4*3*2*1 = 120 ANSWER:E #### E QUESTION:8 bottles need to be arranged togather. 2 of the bottles contain milk and 2 other contain water must sit togather. In how many arrangements can the bottles be arranged? options: A)A.1296 B)B.1850 C)C.2880 D)D.3546 E)E.4200 SOLUTION:Glue milk and water bottlestogether: {AB}, {CD}. 6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each bottle within their unit can be arranged in 2! ways. Therefore the final answer is 6!*2!*2!=2,880. Answer: C. #### C QUESTION:Two trains of length 100 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? options: A)10 sec B)32 sec C)82 sec D)20 sec E)19 sec SOLUTION:Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 100 + 280 = 380m. The time required = d/s = 380/20 = 19 sec. Answer:E #### E QUESTION:How many days will there be from 26th January,1996 to 15th May,1996(both days included)? options: A)102 B)103 C)111 D)120 E)201 SOLUTION:Explanation : Number of days from 26-Jan-1996 to 15-May-1996 (both days included) = 6(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 111 Answer : Option C #### C QUESTION:If a book is sold at 5% profit instead of 5% loss, it would have brought Rs 13 more. Find out the cost price of the book options: A)75 B)72 C)130 D)70 E)80 SOLUTION:Let C.P. of the book be Rs. ’X’ Given, 1.05 X - 0.95X = 13 => 0.1 X = 13 = 13/0.1 = Rs 130 ANSWER:C #### C QUESTION:If x is less than y by 25% then y exceed x by: options: A)33.33% B)25% C)75% D)66.66% E)None of these SOLUTION:Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%) => 25(100-25)*100 =33.33% ANSWER:A #### A QUESTION:The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? options: A)16 2/3% loss B)100/3% loss C)50/3% profit D)100/3% loss E)200/3% loss SOLUTION:Explanation: 15 CP = 18 SP 18 --- 3 CP loss 100 --- ? => 16 2/3% loss ANSWER IS A #### A QUESTION:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points R is in the same quadrant as the fourth vertex of the square? options: A)(-5, -3) B)(-5, 3) C)(5, -3) D)(3, -5) E)(3, 5) SOLUTION:The question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points R is in the same quadrant as the fourth vertex of the square? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. #### E QUESTION:If the product of the integers r, s, t and u is 770, and if 1 < r< s< t< u, what is the value of r+ u? options: A)10 B)13 C)16 D)18 E)21 SOLUTION:770 = 2 * 5 * 7 * 11 So r= 2, s= 5, t= 7, u= 11 r+ u= 2 + 11 = 13 Answer - B #### B QUESTION:3 workers transfer a tool weighing 120kg in 12 seconds. How many men are required to transfer it in 9 seconds? options: A)4 B)5 C)6 D)7 E)8 SOLUTION:We have, M1D1H1 = M2D2H2 3*120*12 = M2*120*9 M2 = 3*120*12/120*9 = 4 ANSWER:A #### A QUESTION:A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 54 years now, the son's age 8 years back was? options: A)12yr B)19yr C)14yr D)10yr E)20yr SOLUTION:Let the son's present age be x years Then, 54-x = x x = 27 Son's age 8 years back = 27-8= 19years Answer is B #### B QUESTION:The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 8480, what is the length of the plot in metres? options: A)20 B)200 C)300 D)90 E)140 SOLUTION:Let length of plot = L meters, then breadth = L - 20 meters and perimeter = 2[L + L - 20] = [4L - 40] meters [4L - 40] * 26.50 = 8480 [4L - 40] = 8480 / 26.50 = 320 4L = 360 L = 360/4= 90 meters. Answer: D #### D QUESTION:There are 35 students in a hostel. If the no. of students increases by 4, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess? options: A)s. 99.75 B)s. 89.75 C)s. 72.75 D)s. 58.75 E)s. 49.75 SOLUTION:Suppose the average join the mess , total expenditure = 35x + 42 Now, the average expenditure = (35x + 42)/ (35 + 4) = x – 1 or, 35x + 42 = 39x – 39 or, x = 20.25 Thus the original expenditure of the mess = 35 x 20.25=708.75 Therefore x-1 = 19.25 hence 42 x 19.25 = 808.50 808.50 - 708.75 = Rs. 99.75 A #### A QUESTION:In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 24. In the company, what is the maximum number of non-managers in a department that has 8 managers? options: A)26 B)27 C)28 D)29 E)30 SOLUTION:8/7 * 24 = 27.4 The answer is B. #### B QUESTION:A sum of Rs. 12500 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest? options: A)4% B)5% C)6% D)8% E)14% SOLUTION:S.I. = (15500 - 12500) = Rs. 3000/- Rate = (100 * 3000) / (12500 * 4) = 6% ANSWER:C #### C QUESTION:In the exam the average was found to be p mark. After deducting typographical error the average marks of 94 student reduced from 84 to 64 . Due to this the average came down by 18.8 marks. What was the number of students who took the exam? options: A)100 B)120 C)110 D)130 E)160 SOLUTION:Explanation : Number of student = (84-64) * 94/18.8 = 100 Answer : A #### A QUESTION:A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000? options: A)Rs.18000 B)Rs.15000 C)Rs.17000 D)Rs.14000 E)NONE SOLUTION:25*12: 30*12: 35*8 15:18:14 14/47 * 47000 = 14000 ANSWER:D #### D QUESTION:A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered? options: A)17% B)18% C)30% D)17% E)12% SOLUTION:Let C.P. be Rs. 100. Then, S.P. = Rs. 123.50 Let the marked price be Rs. x. Then, 95/100 x = 123.50 x = 12350/95 = Rs. 130 Now, S.P. = Rs. 130, C.P. = Rs. 100 Profit % = 30%. Answer: C #### C QUESTION:A store has 10 bottles of juice, including 6 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 2 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought. options: A)1/7 B)1/12 C)1/14 D)1/18 E)1/21 SOLUTION:The total number of ways to sell 6 bottles from 10 is 10C6 = 210. The number of ways to sell 2 bottles of apple juice is 6C2*4C4 = 15*1 = 15 P(selling 2 bottles of apple juice) = 15/210 = 5/70 = 1/14 The answer is C. #### C QUESTION:Find the value of x in (x/5)+3=4. options: A)1 B)2 C)3 D)4 E)5 SOLUTION:(x/5)+3=4. Subtracting both sides with 3 gives x/5=1 Multiplying both sides by 5 gives x=5 Answer: E #### E QUESTION:A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is: options: A)4 mph B)2.5 mph C)3 mph D)2 mph E)None of these SOLUTION:Explanation : Speed of the boat in still water = 10 mph Let speed of the stream be x mph Then, speed downstream = (10+x) mph speed upstream = (10-x) mph Time taken to travel 36 miles upstream - Time taken to travel 36 miles downstream = 90/60 hours =>36/(10−x) − 36/(10+x) = 3/2 =>12/(10−x) − 12/(10+x) = 1/2 =>24(10 + x) − 24(10 − x) = (10 + x)(10 − x) =>240 + 24x − 240 + 24x = (100−x2) =>48x = 100 − x2 =>x2 + 48x − 100 =0 =>(x+50)(x−2)=0 => x = -50 or 2. Answer : Option D #### D QUESTION:Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price? $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239 options: A)0 B)1 C)2 D)3 E)4 SOLUTION:Taking the prices of products in ascending order(already arranged) $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239 we see that median value is the 6th value as there in total 11 values given Arithmetic mean = total/number of entries = 1428/11 =129.8181 We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price as we can clearly see that there is one value between $120 and $129.81, answer is 1 unit Correct Answer - B #### B QUESTION:Find the product of the local value and absolute value of 8 in 564823 options: A)1600 B)6400 C)16000 D)12000 E)18000 SOLUTION:Explanation: Place value = Local value Face value = Absolute value The place value of 8 in 564823 is 8 x 100 = 800 The face value of 8 in 564823 is nothing but 8. => 800*8=6400 Answer: Option B #### B QUESTION:There are 5 different letters and 5 letter boxes of same size shape and colors. How many method are possible to post the letters? options: A)50 B)51 C)52 D)53 E)54 SOLUTION:50000 ->1 41000 ->5 31100 ->10 32000 ->10 21110 ->10 22100 ->15 11111 ->1 1+5+10+10+10+30+1=52 ANSWER:C #### C QUESTION:A rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares? options: A)a) 4 inches B)b) 6 inches C)c) 5 inches D)d) 8 inches E)e) 10 inches SOLUTION:you need to divide the width and length of the rectangular to equal pieces where L = W you can solve this using GCF 35=5*7 45=3*3*5 GCF = 5 P.S you can make squares with side of 5 Answer : C #### C QUESTION:Find the smallest four-digit number which is a multiple of 112. options: A)896 B)1008 C)1120 D)1024 E)None of these SOLUTION:The smallest four digit number is 1000. If 1000 is divided by 112, the remainder is 104. 112 - 104 = 8, if 8 is added to 1000, it will become the smallest four digit number and a multiple of 112. ANSWER:B #### B QUESTION:A man bets on no.16 on a roulette wheel 14times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and istherefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what r the odds of winning on the bet that he takes? options: A)35:1 B)Either ;35:1 C)Either 70;35:1 D)Either 55;45:1 E)Either 65;35:5 SOLUTION:Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans. Either ;35:1 B) #### B QUESTION:There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle. When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left. So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left. Finally, they woke up the 7th thief and this time the diamonds were divided equally. How many diamonds did they steal in total? options: A)1101 B)1141 C)1120 D)1130 E)None SOLUTION:We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60. Answer B #### B QUESTION:How many multiples of 5 are there between 5 to 95? options: A)9 B)18 C)17 D)16 E)15 SOLUTION:As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the unit’s place). So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90. Answer C #### C QUESTION:The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is : options: A)1520 m2 B)2420 m2 C)2480 m2 D)2520 m2 E)None of these SOLUTION:Solution We have : (l - b) = 23 and 2 (l + b) = 206 or (l + b) = 103. Solving the two equations, we get, l = 63 and b = 40. ∴ Area = (l × b) = (63 × 40) m2 = 2520 m2. Answer D #### D QUESTION:City X has a population 5 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z? options: A)1:8 B)1:4 C)2:1 D)4:1 E)10:1 SOLUTION:x= 5y, y= 2*z X : Y , Y : Z 5 : 1 , 2 : 1 10 : 2 , 2 : 1 So, X : Z = 10 : 1 (E) #### E QUESTION:A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is: options: A)130 B)360 C)500 D)540 E)580 SOLUTION:L = 800 m S = 78kmph = 65/3 mps Time to pass tunnel = 1min = 60 sec t.f (800+X)/(60) = (65/3) =500 ANSWER:C #### C QUESTION:A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day? options: A)10 B)41 C)31 D)21 E)22 SOLUTION:Explanation: 1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12 1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16 1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48 Let ‘x’ be the No. of boys required. Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1 = (4 + 3 + x)/48 = 1 i.e. 7 + x= 48 and x = 41. Answer: Option B #### B QUESTION:What will be the cost of building a fence around a square plot with area equal to 144 sq ft, if the price per foot of building the fence is Rs. 58? options: A)2784 B)2287 C)2977 D)2668 E)1298 SOLUTION:Let the side of the square plot be a ft. a2 = 144=> a = 12 Length of the fence = Perimeter of the plot = 4a = 48 ft. Cost of building the fence = 48 * 58 = Rs. 2784. Answer:A #### A QUESTION:An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee? options: A)5 B)10 C)15 D)20 E)25 SOLUTION:Total Employees: 6 Female: 5 Male: 1 committee of 3 with inclusion of Male Number of ways Female can be selected : 5C2 = 10 For male it should be 6C1 or 6C6 6C1= 6 6C6= 1 ANS= 10 B #### B QUESTION:A triangle has sides 10, 17, and 21. A square is inscribed in the triangle. One side of the square lies on the longest side of the triangle. The other two vertices of the square touch the two shorter sides of the triangle. What is the length of the side of the square? options: A)148/29 B)168/29 C)168/26 D)158/29 E)198/29 SOLUTION:By Heron's Formula, the area, A, of a triangle with sides a, b, c is given by A = square root[s(s − a)(s − b)(s − c)], where s = ½(a + b + c) is the semi-perimeter of the triangle. Then s = ½(10 + 17 + 21) = 24, and A = 84. A square inscribed in a 10 by 17 by 21 triangle, with perpendicular dropped onto the side of length 21. Now drop a perpendicular of length h onto the side of length 21. We also have A = ½ × base × perpendicular height. Hence A = 21h/2 = 84, from which h = 8. Notice that the triangle above the square is similar to the whole triangle. (This follows because its base, the top of the square, is parallel to the base of the whole triangle.) Let the square have side of length d. Considering the ratio of altitude to base in each triangle, we have 8/21 = (8 − d)/d = 8/d − 1. Therefore the length of the side of the square is 168/29. ANSWER:B #### B QUESTION:The cost price of 16 articles is the same as the selling price of 12 articles. Find the loss/profit percentages. options: A)30% B)32.50% C)33 1/3% D)40% E)50% SOLUTION:Explanation: The gain is 4 out of 12 articles. Therefore, gain percentage = 4x100/12 = 100/3 = 33 1/3% Answer: Option C #### C QUESTION:A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30 / kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture? options: A)1 kgs B)3 kgs C)5 kgs D)6 kgs E)None of these SOLUTION:Explanation : If the selling price of mixture is Rs.30/kg and the merchant makes a profit of 20%, then the cost price of the mixture = 30/1.2 = Rs.25/kg. We need to find out the ratio in which the three varieties are mixed to obtain a mixture costing Rs.25 /kg. Let variety A cost Rs.20/kg, variety B cost Rs.24 / kg and variety C cost Rs.30/kg. The mean desired price falls between B and C. Step 1: Find out the ratio Qa:Qc using alligation rule. Qa/Qc=(30−25)/(25−20)=1/1. Step 2: Find out the ratio Qb:Qc using alligation rule. Qb/Qc=30−25/(25−24)=5/1. Step 3: Qc is found by adding the value of Qc in step 1 and step 2 =1+1=2. Therefore, the required ratio =1:5:2. If there are 2 kgs of the third variety in the mixture, then there will be 5 kgs of the second variety in the mixture. Answer : C #### C QUESTION:A group of men decided to do a work in 20 days, but 8 of them became absent. If the rest of the group did the work in 28 days, Find the original number of men? options: A)60 B)28 C)40 D)50 E)25 SOLUTION:Original number of men = 8*28 / (28-20) = 28 Answer is B #### B QUESTION:If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between? options: A)0 and 3/20 B)3/20 and 1/5 C)1/5 and 1/4 D)1/4 and 3/10 E)3/10 and 1/2 SOLUTION:A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest. Answer (E) #### E QUESTION:What number is 60 more than two-fourth of itself? options: A)180 B)225 C)288 D)324 E)336 SOLUTION:2/4x+60= x That means 60=2/4x x= 60*3= 180 A is the answer #### A QUESTION:What is the Value given by the equation (-2+a)^2=(a-2)^2? options: A)Indefinite B)Two C)Three D)One E)None SOLUTION:(-2+a)^2=(a-2)^2 Both the equations in RHS and LHS are equal So it give the Value One Option D is answer #### D QUESTION:3,9,27,81,.... options: A)583 B)604 C)616 D)243 E)636 SOLUTION:1*3=3 3*3=9 9*3=27 27*3=81 81*3=243 ANSWER:D #### D QUESTION:A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? options: A)18:11 B)18:18 C)18:22 D)18:39 E)18:39 SOLUTION:Explanation: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. A : B 8000*18 : (8000*4) + (4000*14) 14400 : 88000 A:B = 18:11 Answer:A #### A QUESTION:The average weight of 20 girls increases by 2 kg when a new girl comes in place of one of them weighing 40 kg. What might be the weight of the new girl? options: A)85 kg B)90 kg C)80 kg D)75 kg E)70 kg SOLUTION:Total weight increased = 20 x 2 kg = 40 kg. Weight of new person = 40 + 40 kg =80 kg Answer : C #### C QUESTION:Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be? options: A)9 B)5 C)6 D)2 E)1 SOLUTION:Explanation: x + y = 15 2x – 3y = 5 x = 10 y = 5 Answer: B #### B QUESTION:One out of every 600 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment? options: A)60,000 B)5,000 C)10,000 D)50,000 E)52,000 SOLUTION:20 broken glasses indicates that 10*10= 100 defected bulbs are present. 100 defected bulbs indicates that 100*600= 60,000 light bulbs are present. A is the answer #### A QUESTION:A man can place 6 large boxes or 9 boxes inside a carton. Can you calculate in how many cartons can he place 66 boxes ? options: A)9 B)10 C)11 D)12 E)13 SOLUTION:A 5 cartons for large boxes = 5 * 6 = 30 boxes 4 cartons for small boxes = 4 * 9 = 36 boxes He will need 9 cartons to place 66 boxes. #### A QUESTION:Can you deduce the pattern and find the next number in the series? 7, 15, 27, 99, __? options: A)276 B)277 C)278 D)279 E)None of these SOLUTION:Solution: 277 Explanation: 7 = (1^1 + 2^1 + 3^1) +1 15 = (1^2 + 2^2 + 3^2) +1 37 = (1^3 + 2^3 + 3^3) +1 99 = (1^4 + 2^4 + 3^4) +1 Thus the next number will be (1^5 + 2^5 + 3^5) +1 = 277 Answer B #### B QUESTION:Two friends run the New York City marathon, one friend finishes the marathon in 400 minutes while the second friend finishes the marathon in 625 minutes. What is the ratio of their speed? options: A)10 : 12 B)1 : 2 C)5 :10 D)20 : 25 E)None SOLUTION:Solution Let us name the friends as A and B. = ( Friend A'S speed) : (Friend B's speed) =√b : √a = √400 : √625 = 20 : 25 Answer D #### D QUESTION:A women buys some shoestrips and then 4 times of that she buys packet pins and then 8 times of shoestrips she buys handkerchiefs Finally she has a bill of Rs3.24. She pays for each article as many paise as there are articles(of that particular item).Now whats the number of handkerchiefs? options: A)15 B)16 C)17 D)18 E)19 SOLUTION:16 ANSWER:B #### B QUESTION:If x and y are integers and 4^(x-4) = 4^(y+4), what is y in terms of x? options: A)x - 8 B)x - 5 C)x - 2 D)x + 2 E)x + 6 SOLUTION:Answer: A 4^(x-4) = 4^(y+4) Since the base is the same, I isolated the equations and solved for y. x-4 = y+4 y=x-8 #### A QUESTION:During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? options: A)80% B)107% C)116.7% D)120% E)140% SOLUTION:Kim purchased 20 gallons of gas. She paid for 5 + 0.9*15 = 18.5 gallons, so the overall discount she got was 1.5/20 = 7.5%. Isabella purchased 25 gallons of gas. She paid for 5 + 0.9*20 = 23 gallons, so the overall discount she got was .5/25 = 8%. 8 is 8/7.5*100 = 107% of 7.5. Answer: B. #### B QUESTION:A sum of Rs.48000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. options: A)28880 B)31200 C)28770 D)29990 E)12770 SOLUTION:Let A be the amount received at the end of the three years. A = 48000[1 + 10/100][1 + 20/100][1 + 25/100] A = (48000 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.79200 So the interest = 79200 - 48000 = Rs.31200 Answer: B #### B QUESTION:The price of commodity X increases by 45 cents every year, while the price of commodity Y increases by 20 cents every year. In 2001, the price of commodity X was $5.20 and the price of commodity Y was $7.30. In which year will the price of commodity X be 35 cents less than the price of commodity Y? options: A)2006 B)2007 C)2008 D)2009 E)2010 SOLUTION:The price of commodity X increases 25 cents each year relative to commodity Y. The price difference is $2.10 and commodity X needs to be 35 cents less than commodity Y. $1.75 / 25 cents = 7 years The answer is 2001 + 7 years = 2008. The answer is C. #### C QUESTION:Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made? options: A)Rs. 13.50 B)Rs. 16.54 C)Rs. 16.80 D)Rs. 16.50 E)Rs. 16.00 SOLUTION:Explanation: Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50 Answer: Option D #### D QUESTION:A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 2 rows or 7 rows or 9 rows, then no tree will be left. Find the least number of trees required options: A)22 B)60 C)126 D)76 E)21 SOLUTION:Explanation: The least number of trees that are required = LCM(2, 7, 9) = 126 Answer: C #### C QUESTION:Evaluate combination 100C100 options: A)10000 B)1000 C)10 D)1 E)0 SOLUTION:Explanation: nCn=1 100C100=1 Option D #### D <<<Examples ends QUESTION:When the positive integer c is divided by 11, the quotient is d and the remainder 3. When c is divided by 19, the remainder is also 3. What is the remainder when d is divided by 19? options: A)4 B)3 C)2 D)1 E)0 SOLUTION:Any Number which when divided by divisor d1,d2, etc. leaving same remainderrtakes the form ofK+r where k = LCM (d1,d2) In this case the divisors are 1119 and remainder is 3. so LCM (11,19) = 209 So N= 209+3 = 212 Also c=d1q+3 ; which means d1q=209d1=11 therefore q=19 And ( d divided by 19)19/19 leaves remainder 0. Answer is E #### E

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